U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2013–5114

A Model for Evaluating Effects of Climate, Water Availability, 

and Water Management on Wetland Impoundments—A 

Case Study on Bowdoin, Long Lake, and Sand Lake National 

Wildlife Refuges
Cover. Lake Bowdoin, Bowdoin National Wildlife Refuge, Montana, October 2011.
A Model for Evaluating Effects of Climate, 

Water Availability, and Water Management 

on Wetland Impoundments—A Case Study 

on Bowdoin, Long Lake, and Sand Lake 

National Wildlife Refuges

By Brian A. Tangen, Robert A. Gleason, and John F. Stamm

Scientific Investigations Report 2013–5114

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Tangen, B.A., Gleason, R.A., and Stamm, J.F., 2013, A model for evaluating effects of climate, water availability, 

and water management on wetland impoundments—A case study on Bowdoin, Long Lake, and Sand Lake National 

Wildlife Refuges: U.S. Geological Survey Scientific Investigations Report 2013–5114, 37 p., http://pubs.usgs.gov/

sir/2013/5114/.
iii

Contents

Acknowledgments........................................................................................................................................vi

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................2

Climate Trends and Projections..........................................................................................................3

Wetland Management on Federal Lands..........................................................................................3

Background and Previous Work ........................................................................................................4

Approach and Methods................................................................................................................................4

Model Structure....................................................................................................................................4

Model Validation Methods and Study Sites .....................................................................................6

Bowdoin National Wildlife Refuge............................................................................................6

Physical Setting ..................................................................................................................6

Water Resources ................................................................................................................8

Management and Environmental Concerns...................................................................8

Model Inputs........................................................................................................................8

Long Lake National Wildlife Refuge .........................................................................................9

Physical Setting ..................................................................................................................9

Water Resources ..............................................................................................................11

Management and Environmental Concerns.................................................................11

Model Inputs......................................................................................................................11

Sand Lake National Wildlife Refuge.......................................................................................12

Physical Setting ................................................................................................................12

Water Resources ..............................................................................................................12

Management and Environmental Concerns.................................................................12

Model Inputs......................................................................................................................12

Model Application...............................................................................................................................15

Overview......................................................................................................................................15

Methods.......................................................................................................................................16

Model Simulation..............................................................................................................16

Model Inputs......................................................................................................................16

Simulated Future Climate Inputs ....................................................................................17

Validation and Application of the Water and Salt Balance Model......................................................18

Results of Model Validation ..............................................................................................................18

Bowdoin National Wildlife Refuge..........................................................................................18

Long Lake National Wildlife Refuge .......................................................................................20

Sand Lake National Wildlife Refuge.......................................................................................20

Discussion of Model Validation...............................................................................................21

Results of Model Application to Bowdoin National Wildlife Refuge .........................................23

Simulation Results .....................................................................................................................23

Discussion of Model Application ............................................................................................24

Summary and Conclusions.........................................................................................................................29

References Cited..........................................................................................................................................30

Appendixes ...................................................................................................................................................33
iv

Figures

1. Map showing location of Bowdoin, Long Lake, and Sand Lake National Wildlife

Refuges in the northern Great Plains ........................................................................................2

2. Graph showing relations between specific conductance and total dissolved solids ......5

3. Map showing location and primary management units of Bowdoin National

Wildlife Refuge..............................................................................................................................7

4. Graph showing Lake Bowdoin pool elevations and stream discharge from Beaver

Creek during 2010 and 2011.........................................................................................................9

5. Map showing location and primary management units of Long Lake National

Wildlife Refuge ...........................................................................................................................10

6. Map showing location and primary management units of Sand Lake National

Wildlife Refuge............................................................................................................................13

7. Graph showing Palmer Modified Drought Index values for northeastern South

Dakota and discharge for the James River from October 1, 1981, to June 1, 2012..........14

8. Graph showing Palmer Modified Drought Index values for north-central Montana

and mean monthly specific conductance for Lake Bowdoin..............................................16

9. Graphs showing outputs from the Weather Research and Forecasting model

simulation.....................................................................................................................................17

10. Graph showing modeled and measured pool elevation and specific conductance

for Lake Bowdoin from May 14 to November 9, 2010, and May 10 to October 25,

2011 ..............................................................................................................................................18

11. Graph showing modeled mean water depth and surface areas for Lake Bowdoin

from May 14 to November 9, 2010, and May 10 to October 25, 2011 ..................................19

12. Graph showing modeled and measured pool elevation and specific conductance

for Unit 1 of Long Lake National Wildlife Refuge from April 23 to November 19,

2010, and May 11 to October 26, 2011......................................................................................20

13. Graph showing modeled mean water depth and surface areas for Unit 1 of Long

Lake National Wildlife Refuge from April 23 to November 19, 2010, and May 11 to

October 26, 2011..........................................................................................................................21

14. Graph showing modeled and measured pool elevation and specific conductance

for Sand Lake National Wildlife Refuge from May 17 to November 22, 2010, and

May 12 to October 27, 2011 .......................................................................................................22

15. Graph showing modeled mean water depth and surface areas for Sand Lake

National Wildlife Refuge from May 17 to November 22, 2010, and May 12 to

October 27, 2011..........................................................................................................................23

16. Graphs showing results from the 50-year model simulations of Lake Bowdoin..............25

17. Graphs showing results from the single-year model simulations of Lake Bowdoin.......26

18. Graphs showing results from the 50-year model simulations of Lake Bowdoin that

included Beaver Creek floods ..................................................................................................27

19. Graph showing specific conductance from the 50-year model simulations of Lake

Bowdoin overlain with salinity category boundaries ...........................................................28

20. Graph showing specific conductance from the 50-year model simulations of Lake

Bowdoin that included Beaver Creek floods overlain with salinity category

boundaries ...................................................................................................................................28
v

Table

1. Summary statistics comparing measured values to the 2010 and 2011 model

simulations of Bowdoin, Long Lake, and Sand Lake National Wildlife Refuges..............19

Conversion Factors and Datums

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2) 

acre 0.004047 square kilometer (km2)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

acre-foot (acre-ft) 0.001233 cubic hectometer (hm3) 

Flow rate

acre-foot per day (acre-ft/d) 0.01427 cubic meter per second (m3/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Mass

ton, short (2,000 lb) 0.9072 megagram (Mg) 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

 °F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

 °C=(°F-32)/1.8

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 

25 °C).

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) 

or micrograms per liter (μg/L).
vi

Acknowledgments

Funding for this project was provided by the U.S. Geological Survey (USGS). We thank Charles 

Dahl and Raymond Finocchiaro for assisting with field work and Betty Euliss for geographic 

information system support. We thank and Jason Alexander and Peter McCarthy for comments 

on a previous version of this report.

We thank all of the staff from Bowdoin, Long Lake, and Sand Lake National Wildlife Refuges for 

providing expertise, data, and field assistance throughout the duration of this project. This work 

would not have been possible without their support and cooperation. Stan Jones, hydrologist 

with Montana Department of Natural Resources and Conservation, converted the original Hamilton and others (1989) model to an Excel format, and we thank Stan and John Simpson (U.S. Fish 

and Wildlife Service) for providing information pertaining to this converted model. Lastly, we 

thank Murray Laubhan for comments on a previous version of this report.
A Model for Evaluating Effects of Climate, Water 

Availability, and Water Management on Wetland 

Impoundments—A Case Study on Bowdoin, Long 

Lake, and Sand Lake National Wildlife Refuges

By Brian A. Tangen, Robert A. Gleason, and John F. Stamm

Abstract

Many wetland impoundments managed by the U.S. Fish 

and Wildlife Service (USFWS) National Wildlife Refuge 

System throughout the northern Great Plains rely on rivers 

as a primary water source. A large number of these impoundments currently are being stressed from changes in water 

supplies and quality, and these problems are forecast to 

worsen because of projected changes to climate and land use. 

For example, many managed wetlands in arid regions have 

become degraded owing to the long-term accumulation of salts 

and increased salinity associated with evapotranspiration. A 

primary goal of the USFWS is to provide aquatic habitats for a 

diversity of waterbirds; thus, wetland managers would benefit 

from a tool that facilitates evaluation of wetland habitat quality in response to current and anticipated impacts of altered 

hydrology and salt balances caused by factors such as climate 

change, water availability, and management actions.

A spreadsheet model that simulates the overall water and 

salinity balance (WSB model) of managed wetland impoundments is presented. The WSB model depicts various habitat 

metrics, such as water depth, salinity, and surface areas (inundated, dry), which can be used to evaluate alternative management actions under various water-availability and climate 

scenarios. The WSB model uses widely available spreadsheet 

software, is relatively simple to use, relies on widely available inputs, and is readily adaptable to specific locations. The 

WSB model was validated using data from three National 

Wildlife Refuges with direct and indirect connections to water 

resources associated with rivers, and common data limitations 

are highlighted. The WSB model also was used to conduct 

simulations based on hypothetical climate and management 

scenarios to demonstrate the utility of the model for evaluating alternative management strategies and climate futures. The 

WSB model worked well across a range of National Wildlife 

Refuges and could be a valuable tool for USFWS staff when 

evaluating system state and management alternatives and 

establishing long-term goals and objectives.

Introduction

The U.S. Fish and Wildlife Service’s (USFWS) National 

Wildlife Refuge System (NWRS) encompasses over 150 million acres of diverse aquatic and terrestrial habitats throughout 

the United States that support a rich variety of wildlife and 

are critical to sustaining much of the Nation’s biotic diversity. In the northern Great Plains (fig. 1), a large number of 

national wildlife refuges (NWR) were established during the 

drought years of the 1930s to provide sanctuary and breeding 

ground for migratory birds and other wildlife. Accordingly, a 

substantial number of these NWRs were located in river flood 

plains, and many contain managed lakes or impoundments that 

require inflows or diversions from lotic systems for primary 

water supply. Hence, the original design and placement of 

many NWRs and managed impoundments were influenced 

by climatic variation and the selection of these sites was 

predicated on the long-term availability of water from reliable 

sources.

Changes in climate can affect natural wetland and terrestrial ecosystems, as well as industry (for example, agriculture, 

forestry, fisheries) and municipalities (Field and others, 2007). 

Recently, widespread concerns over global climate change 

have prompted syntheses of research on the mechanisms of 

change (Solomon and others, 2007) and the potential effects 

to ecological systems in the United States and northern Great 

Plains (Bridgham and others, 1995; Field and others, 2007; 

Brekke and others, 2009; Karl and others, 2009; Johnson 

and others, 2010). The most direct links between climate and 

aquatic ecosystems are hydrology and phenology. Changes 

in climate would potentially alter the hydrologic budget on 

a range of scales, from small wetlands (Johnson and others, 

2010) to larger watersheds and their associated lakes and 

streams. Similarly, changes in regional temperature patterns 

associated with climate change would have a variety of effects 

ranging from altered rates of evapotranspiration to a shift in 

the timing of snowfall and spring snowmelt. Such changes 

could subsequently affect plant phenology, primary and 
2 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

secondary production, and ultimately, the distribution and size 

of wildlife populations (Field and others, 2007). Moreover, 

these types of direct impacts can be exacerbated through interactions with indirect effects associated with wetland management and ecosystem change.

Purpose and Scope

The purpose of this report was to establish the framework for a tool that could be used to assess the state of an 

impoundment and impacts of climate or management on 

specific habitat and water-quality parameters. The proposed 

model framework uses a water and mass balance approach 

to simulate water and salinity levels of individual managed 

impoundments, which regulate various habitat (for example, 

water depth, salinity, inundated and dry surface areas) and 

water-quality characteristics.

Three NWRs were selected to test and validate the 

proposed model: Bowdoin NWR (BNWR) (Montana), Long 

Lake NWR (LLNWR) (North Dakota), and Sand Lake NWR 

(SLNWR) (South Dakota) (fig. 1). However, the models and 

concepts discussed throughout this report are applicable to 

managed impoundments throughout the NWRS. The refuges 

considered for this report span the regional precipitation 

gradient that increases from west to east, have direct and 

indirect relations to water resources associated with rivers, and 

are influenced by rivers with downward, neutral, or upward 

streamflow trends over approximately the past 50 years 

(Anderson and Norton, 2007; Anderson and others, 2008).

Figure 1. Location of Bowdoin, Long Lake, and Sand Lake National Wildlife Refuges (NWR) in the northern Great Plains.

Yellowstone

Missouri

Souris

Red River of the North

108° 104° 100°

50°

48°

46°

44°

Long Lake NWR

Base from Environmental Systems Research Institute, Inc., 2006,

various scales and Montana Natural Resource Information System, 

various dates and scales, 

Universal Transverse Mercator, zone 13N,

Central Meridian -105.0000000

North American Datum of 1983 

Sand Lake NWR

Bowdoin NWR

NORTH DAKOTA

SOUTH DAKOTA

MONTANA

0 75 150 300 Miles

Kilometers

MILES

0 75 150 300 KILOMETERS
Introduction 3

Climate Trends and Projections

Climate trends in the United States indicate that precipitation and average temperature have increased over the past 

50 years, but these trends vary greatly among regions (Anderson and Woosley, 2005; Karl and others, 2009). The northern 

Great Plains region of the United States (fig. 1) is characterized by an increasing precipitation gradient from west to east. 

Observed trends in the region for the 50-year period from 

1958 to 2008 indicate that the Dakotas and Minnesota are 

becoming wetter and Montana is becoming drier. Average temperatures in the region have increased over the same period 

(Karl and others, 2009). Anderson and Woosley (2005) suggest downward trends in precipitation since 1971 for Montana, 

Wyoming, western North Dakota, and western and southern 

Nebraska, and upward trends in South Dakota, southeastern 

North Dakota, and northeastern Nebraska. Badh and Akyuz 

(2010) examined precipitation records from eight stations in 

North Dakota and did not identify an overall trend in annual 

precipitation. Millett and others (2009) evaluated climate 

trends from 1906 to 2000 at 18 climate stations in the Prairie 

Pothole Region. Precipitation increased by 1.9 inches (in.) 

(9 percent) with all of the significant increases (10 stations) 

located in the eastern part of the Prairie Pothole Region, and 

minimum daily temperature increased 1.8 degrees Fahrenheit 

(°F) and maximum daily temperature decreased 0.36 °F (Millett and others, 2009). Karl and others (2009, p. 28) estimate 

that average temperature from 1993 to 2008 in the Missouri 

River drainage basin was 1.08 to 3.06 °F warmer than the 

average for 1961–1979, with greatest warming in areas of the 

northern Missouri River watershed.

Climate projections for the Great Plains forecast 

increased temperatures and precipitation in the north, and forecast a higher frequency of extreme weather and climate events, 

such as heavy precipitation or extended drought, throughout 

the region (Karl and others, 2009). Additionally, the percentage of precipitation depositing as snow may decrease, and 

the typical timing of spring snowmelt could shift. Moreover, 

Markstrom and others (2012) predict a steady increase in 

minimum and maximum temperatures throughout the 21st 

century over the range of greenhouse gas emission scenarios 

evaluated.

Wetland Management on Federal Lands

The USFWS typically manages wetland impoundments 

according to habitat objectives that are based on providing the 

life requisites of a specific suite of taxa, which often vary by 

season. For example, spring water levels in an impoundment 

may be increased to provide optimal nesting and roosting habitat for colonial-nesting waterbirds and lowered in the fall to 

provide foraging habitat for fall migrating shorebirds. Wetland 

managers also may use water-level manipulations or flushing 

to alleviate water-quality problems or alter vegetation communities. For example, wetland water levels may be lowered to 

encourage deflation of salts (removal by wind) from exposed 

sediments, or influxes of freshwater during floods may be used 

to flush accumulated salts. Similarly, undesirable monotypic 

stands of cattail (Typha sp.) can be diminished by increasing 

water levels for extended periods of time, or influxes of freshwater at specific times can reduce salinity levels and encourage germination of freshwater vegetation.

Projected climate-driven alterations to water availability 

may limit flexibility to achieve specific habitat objectives or 

require modifications to account for shifting climate patterns. 

For instance, changes in the timing or intensity of precipitation, snowmelt, or springtime river flows may constrain the 

ability to implement desired water-level manipulations, and 

higher temperatures and longer growing seasons could result 

in greater water losses through evapotranspiration, which 

could substantially alter the seasonal water balance of an 

impoundment. Various climate-related impacts that constrain 

a manager’s ability to manipulate the water level of impoundments could result in changes to vegetative habitat conditions 

(plant community composition, structure, and distribution) 

and water chemistry. Increases or decreases in the amount of 

water delivered to a system may result in a shift of the ratio 

between open water, emergent vegetation, and mudflats; and 

concentrations of salts or harmful elements (for example, 

trace metals) can change drastically in response to dilution or 

evapoconcentration.

Historically, climate patterns in the northern Great Plains 

have alternated between wet and dry periods with no identifiable frequency of cycles, but droughts have persisted for 

longer periods in interior sections of the country than sections 

closer to the coast (Karl and Koscielny, 1982). As such, the 

USFWS has developed flexible management objectives to capitalize on this natural variation. For example, during dry periods wetland managers may reduce water levels to the greatest 

extent possible to encourage nutrient cycling and changes 

in plant community composition and structure. However, 

because of uncertainties pertaining to future climate trends and 

water supplies, current management objectives may have to 

be modified or new ones developed. Thus, wetland managers 

would benefit from a tool for assessing the effects of projected 

changes in climate and water availability on their ability to 

achieve current or alternative management objectives.

The primary purpose for modeling habitat characteristics 

of wetland impoundments, from a conservation manager’s 

perspective, is to determine the most appropriate allocation 

of water resources based on biological goals, potential water 

availability, and climate conditions. The overarching goal is to 

provide habitat conditions that support and sustain target wildlife populations such as migratory waterbirds. For instance, 

many waterbirds exhibit optimal water depths for foraging, 

preferences for food resources that often vary seasonally, and 

require certain vegetation conditions (distribution, height, 

cover) to successfully complete critical life-history events 

such as breeding and migration (Swanson and others, 1974; 

Fredrickson, 1991; Skagen and Knopf, 1994; Colwell and Taft, 

2000; Laubhan and others, 2006; Niemuth and others, 2006; 
4 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Ma and others, 2010); all factors that can be manipulated 

through water management. Similarly, most aquatic plants and 

invertebrates, which provide critical food and habitat resources 

for waterbirds, are linked to optimal salinity levels or water 

depths (Stewart and Kantrud, 1972; Hammer and Heseltine, 

1988; Baskin and Baskin, 1998; Laubhan and others, 2006; 

Gleason and others, 2009).

Background and Previous Work

A multitude of approaches have been applied to evaluate the effects of land use, climate, water availability, and 

water allocation to the water balance of wetlands, lakes, and 

drainage basins (Hamilton and others, 1989; Poiani and others, 

1996; Kendy, 1999; Su and others, 2000; Vining, 2007; Markstrom and others, 2012; Nimick and others, 2011). This project 

required a model capable of simulating the water and salt budget of managed impoundments and that provides outputs that 

can be related to habitat quality. Examples of common models 

and tools that have been well-vetted and are readily available 

as software packages include the Precipitation-Runoff Modeling System (PRMS; Leavesley and others, 1983) and the Soil 

& Water Assessment Tool (SWAT; Neitsch and others, 2011). 

However, use of these software-based models often requires 

specialized training or computer expertise, and they can be difficult to customize. Further, required data often are not readily 

available or must be manipulated prior to input.

No software packages were identified that provided the 

desired model outputs, so an existing model framework was 

simplified and developed in Microsoft Excel. The water and 

salinity balance (WSB) model developed for this study is 

based on a water and salt balance model for BNWR that was 

developed by Hamilton and others (1989) and later applied 

by Kendy (1999). The Hamilton and others (1989) model 

originally was written in standard FORTRAN and executed 

within a control system. In partnership with the USFWS, the 

Montana Department of Natural Resources and Conservation 

(MDNRC) converted this model for operation in Excel to conduct assessments of proposed management actions at BNWR 

(U.S. Fish and Wildlife Service, 2011). The WSB model 

framework presented in this report was modified from the 

MDNRC effort. The WSB model relies on widely available 

inputs, is easily adaptable, and provides desired outputs such 

as water level and specific conductance. Further, the WSB 

model is straightforward, transparent, and runs using standard 

spreadsheet software so it can easily be used as a tool to evaluate alternative management objectives for specific locations.

Approach and Methods

Model Structure

The Hamilton and others (1989) model incorporates 

water inputs from precipitation, numerous sources of surface 

water (for example, irrigation canal and surface runoff) and 

groundwater seeps. Water losses are attributed to evaporation, 

surface outflows, and seepage. The salt balance includes ions 

associated with the water sources, as well as salts that diffuse 

upward from the lake sediments and precipitate out of solution as water levels decline. This original model is very site 

specific, includes numerous variables that have to be estimated 

(for example, groundwater seepage and surface runoff), and is 

overly complex for some needs. Therefore, the Hamilton and 

others (1989) model was simplified to include only the primary sources and losses of water and salt, as well as variables 

that can be directly measured or predicted using currently 

available data. By simplifying this model, there is potential 

to lose some precision, but the inherent error was reduced 

by eliminating multiple factors (for example, groundwater 

interactions) that require estimation. Because the proposed 

model does consider the primary sources and losses, it should 

adequately capture overall trends required to evaluate management objectives and strategies. Moreover, the proposed model 

is easily modified to include additional variables when data are 

available.

The simple WSB model accounts for the primary sources 

and losses of water and salts associated with a given managed impoundment: direct precipitation, influx from rivers 

(regulated or unregulated), “other” surface-water influx (for 

example, inter-unit transfers), evapotranspiration (ET), and 

surface-water outflows. The combined overall WSB model is 

as follows:

ΔV = P + SWI - ET - SWO

ΔS = PS + SWIS - SWOS

where ΔV is change in water volume (V) stored in the 

impoundment,

ΔS is change in mass of salts (S) in water volume 

(V),

P is precipitation that falls directly on the 

inundated part of the impoundment,

PS ismass of salts (S) in precipitation (P),

SWI is water transferred into the impoundment 

through surface water input,

SWIS is mass of salts (S) in surface water inputs 

(SWI),

ET is water evapotranspiration from the 

inundated part of the impoundment,

SWO is water transferred out of the impoundment 

by surface-water outflow, and

SWOS is mass of salts (S) in surface-water outflow 

(SWO).

Specific conductance and surface-water (pool) elevation 

values are required to set initial impoundment conditions, and 

the WSB model requires a surface area-capacity-depth curve 

for the impoundment. Inputs and losses (water and salt) are 

calculated using precipitation, temperature, solar radiation, 
Approach and Methods 5

managed or unmanaged surface flows (rate and specific 

conductance of inflows/outflows), and management information (for example, elevation of water-control structures) at the 

desired temporal scale (for example, daily, monthly).

Once the initial conditions are input, the WSB model calculates the starting volume of water, surface areas (inundated 

and dry), mean depth for the impoundment, and mass of salts 

in the impoundment. The inundated surface area is defined as 

the part of the impoundment with standing water, and the dry 

surface area is the difference between the maximum area and 

the area that is inundated. The dry surface area could be mud 

flats or emergent or riparian vegetation. Volume, areas, and 

mean depth are based on the surface area-capacity-depth curve, 

and mass of salts is calculated by using a regression model to 

convert specific conductance (microsiemens per centimeter at 

25 degress Celsius [μS/cm]) to total dissolved solids (TDS; 

milligrams per liter [mg/L]), which is adjusted for wetland 

volume. Models relating specific conductance and TDS (fig. 2) 

can be obtained from the literature or developed by collecting site-specific data. The mass of salts gained or lost from the 

impoundment is determined based on specific conductance 

of the inflows and outflows. Volume of water associated with 

direct precipitation and ET is determined by adjusting for the 

inundated area of the impoundment. Thereafter, the daily water 

balance for the impoundment is determined by adding the volume of water from direct precipitation and surface inflows and 

subtracting losses to ET and surface outflows.

When the calculated daily volume exceeds the maximum 

volume established by the height of the water-control structure, or when the water-control structure elevation is lowered, 

the excess volume of water (and associated salts) is treated 

as surface outflow that is completely removed at a daily time 

step. In reality, when an impoundment’s volume exceeds its 

capacity, rate of water outflow is regulated by channel dimensions, topography, depth, and flow pathways. Thus, relations 

between pool elevation (stage) and discharge, when available, 

can greatly improve model performance by incorporating 

more accurate estimates of outflow rates (including interunit 

transfers between management units). These stage-discharge 

curves are less important for closed-basin type systems with 

limited outflow (for example, BNWR) but are critical for flowthrough type systems where an accurate accounting of both 

inflows and outflows is essential (for example, LLNWR and 

SLNWR).

The WSB model outputs include variables such as pool 

elevation, mean water depth, inundated and dry surface area, 

and specific conductance, which can all be used to assess habitat or management objectives. The WSB spreadsheet model is 

designed to run at a daily time step but can easily be modified to run at other time intervals. Further, the WSB model 

is designed to run for a single growing season but can be run 

over consecutive years by estimating winter precipitation, 

evaporation/sublimation, and inflows from spring snowmelt 

runoff.

Tchobanoglous and Burton, 1991 

Long Lake National Wildlife Refuge, unpublished 

Kendy, 1999 

Hamilton and others, 1989 

Swanson and others, 1988 

EXPLANATION

Total dissolved solids, in milligrams per liter

Specific conductance, in microsiemens per centimeter at 25 degrees Celsius 100,000

120,000

140,000

160,000

20,000

40,000

60,000

80,000

0

0 20,000 40,000 60,000 80,000 100,000

Figure 2. Relations between specific conductance and total dissolved solids.
6 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

The WSB model determines daily outflow volume by 

calculating the difference between the modeled volume and 

the maximum volume based on the water-control structure 

elevation and incorporating any managed outflows by the 

use of canals or pumps. However, the WSB model structure 

allows for the incorporation of stage-discharge curves when 

available. The WSB model calculates potential ET using the 

Jensen-Haise equation (Jensen and Haise, 1963; McGuinness and Bordne, 1972; Rosenberry and others, 2004), 

which requires temperature and solar radiation as inputs. Pan 

evaporation (Hamilton and others, 1989; Kendy, 1999; Nimick 

and others, 2011) or other equations (Winter and Rosenberry, 

1995; Rosenberry and others, 2004) can be easily substituted 

depending on the availability of input data. All WSB model 

variables and calculations are described in appendix 1 and 

general instructions for the WSB model are presented in 

appendix 2. An Excel version of the WSB spreadsheet model 

is available at http://pubs.usgs.gov/sir/2013/5114/.

Model Validation Methods and Study Sites

To test and validate the WSB model, data were collected 

for three NWRs: BNWR, LLNWR, and SLNWR. All three 

NWRs were established during the dustbowl years of the 

1930s with the goal of providing sustainable wetland habitats 

for migratory birds and other wildlife. The managed lakes of 

these refuges all rely, to varying degrees, on the timing and 

amount of water delivered from river systems to meet various 

water-quality, habitat, and management goals. Overviews are 

provided for each refuge in the following sections. Additional 

details about each NWR can be found in their respective Comprehensive Conservation Plans (CCP) (U.S. Fish and Wildlife 

Service, 2012a) and web sites (U.S. Fish and Wildlife Service, 

2012b).

Model input and validation data were collected during 

the majority of the ice-free seasons of 2010 and 2011. Information for daily model inputs was collected where available 

on precipitation, temperature, solar radiation, surface-water 

inflows and outflows, and specific conductance of the inflow/

outflow waters. Surface area-capacity-depth curves also were 

obtained for each NWR. Additionally, each impoundment 

was instrumented with pressure transducers equipped with a 

conductivity sensor to collect continuous measurements of 

specific conductance and water depth, which was converted to 

pool elevation. Mean specific conductance and pool elevation 

were determined using daily values obtained from data loggers distributed around each impoundment. Data loggers were 

strategically distributed around each impoundment to capture 

potential spatial variation in specific conductance or pool 

elevation. Placement of the data loggers was based on previously collected data and knowledge of each impoundment, 

as well as accessibility. For BNWR, specific conductance 

and pool elevation represent a mean from three data loggers 

distributed around Lake Bowdoin during 2010 (May 14–

November 9) and 2011 (May 10–October 25). For SLNWR, 

specific conductance and pool elevation represent a mean from 

five (2010) and six (2011) data loggers distributed around 

Mud and Sand Lakes during 2010 (May 17–November 22) 

and 2011 (May 12–October 27), respectively. For LLNWR, 

specific conductance and pool elevation represent values from 

a single logger located near the outlet of Unit 1 during 2010 

(April 23–November 19) and 2011 (May 11–October 26). 

Additional data were collected from the other management 

units of LLNWR, but they were not used in the WSB model 

validation.

The WSB model was adapted to each refuge and was run 

using starting values and inputs collected during data-logger 

deployment during 2010 and 2011. Results were compared to 

measured specific conductance and pool elevation to evaluate the WSB model performance for the dates that the data 

loggers were installed. Specifically, the average daily absolute 

difference between modeled and measured pool elevation and 

specific conductance was calculated, and the percentages of 

the modeled depth and measured specific conductance that 

these absolute differences represent were determined. For pool 

elevation, percentages were based on modeled data because 

a measured mean water depth for the impoundments was not 

available. The WSB model also provides estimates of mean 

depth and inundated and dry surface areas; these variables are 

calculated using the surface area-capacity-depth curves, and 

data to assess their precision were not collected because of 

time and budgetary constraints.

Bowdoin National Wildlife Refuge

BNWR is located in the Milk River Valley of north-central Montana (fig. 3). This area is a relatively arid (annual precipitation, 10–14 in.) region associated with downward trends 

in river flow over approximately the past 50 years (Anderson 

and Norton, 2007; Anderson and others, 2008). Managed 

wetland impoundments on BNWR rely heavily on water from 

the Milk River supplied through a manmade canal; thus, the 

refuge has an indirect connection to a river. BNWR was established in 1936 to provide habitat and refuge for migrating and 

nesting birds and other wildlife; today, it supports thousands 

of waterfowl, shorebirds, and colonial nesting waterbirds. The 

refuge has been widely recognized for its habitats and great 

value to migratory birds and has been included in the Western 

Hemisphere Shorebird Reserve Network and designated as a 

Globally Important Bird Area.

Physical Setting

BNWR covers approximately 15,500 acres and includes 

approximately 8,675 acres of freshwater and saline wetlands 

interspersed among mixed-grass prairie. Aquatic habitats 

on the refuge include five shallow lakes, the largest being 

the 5,459-acre Lake Bowdoin and the 1,200-acre Dry Lake 

(fig. 3). The refuge lakes and wetlands are divided by an 

array of dikes, roads, and a railroad bed; management and 

water transfers are accomplished through use of various 
Approach and Methods 7

Figure 3. Location and primary management units of Bowdoin National Wildlife Refuge.

#

#

#

#

107°44’ 107°36’

48°32’

48°24’

48°16’

MONTANA

Study area

Rocky Mountains

Milk River

Fort Peck

Lake

Nelson Reservoir

Lake Bowdoin

Dry Lake

Pond

Dry Lake

Unit

Drumbo Unit

Lakeside Unit

Lakeside Extension

Milk River

Beaver Creek

Dodson South Canal

Bowdoin

 National

 Wildlife

 Refuge

X

EXPLANATION

Weather Station

#

X

Data logger

# U.S. Geological Survey

stream gage

Base from Environmental Systems Research Institute, Inc., 2006, various scales 

and Montana Natural Resource Information System, various dates and scales

Universal Transverse Mercator, zone 13N,

Central Meridian -105.0000000

North American Datum of 1983

0 1.75 3.5 7 MILES

0 1.75 3.5 7 KILOMETERS

MissouriRiver
8 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

water-control structures and ditches. Water levels fluctuate in 

response to water delivery, but average depths are less than 

3.5 feet (ft).

Water Resources

Prior to European settlement, Lake Bowdoin likely functioned as a flowthrough wetland that released water to Beaver 

Creek. The refuge occupies a low point in the landscape, and 

with the additions of dikes and water-control structures, Lake 

Bowdoin currently functions as a closed-basin hydrologic 

sump with very limited surface outflow (for example, during Beaver Creek floods). The primary natural water sources 

for Lake Bowdoin are precipitation, runoff from the Black 

Coulee drainage (not shown on figure 3; enters the refuge 

near southwest arm of Lake Bowdoin), and episodic overbank 

flooding from neighboring Beaver Creek. Groundwater seeps 

also can contribute a relatively small amount of water to the 

lake (Kendy, 1999). These natural sources of water have been 

augmented by an annual allocation to the refuge of at least 

3,500 acre-feet (acre-ft) from the Milk River through the 

Dodson South Canal, a component of the Bureau of Reclamation’s Milk River Irrigation Project, and irrigation return flows 

from surrounding agricultural lands. The primary water loss is 

evaporation, which is more than double the average precipitation (greater than 24 and 12 in., respectively) on an annual 

basis (U.S. Fish and Wildlife Service, 2011). Water typically is 

not released downstream to Beaver Creek because of waterquality (salinity) concerns.

Management and Environmental Concerns

Historically, Lake Bowdoin presumably exhibited 

dynamic salinity levels that fluctuated in response to climatic 

cycles and floods. Early settlers greatly modified the landscape, shifting the lake primarily to a closed-basin system. 

Prior to establishment of BNWR, the lake was used by the 

Bureau of Reclamation to collect irrigation return flows and 

excess water from the Milk River project. After establishment 

of the refuge, the USFWS managed Lake Bowdoin to optimize 

habitat for waterfowl and other waterbirds, which resulted 

in the retention of all available water. The additions of more 

saline inflows, such as irrigation return flows, combined with 

management strategies to limit the amount of water exported 

from the lake and a negative precipitation-evaporation ratio 

led to the accumulation of salts and increased TDS concentrations over time.

During the 1970s, the USFWS recognized salinity was 

beginning to increase in Lake Bowdoin and Dry Lake, and 

since that time a primary focus of refuge staff is the management of salts. Currently, the main issues are deflation from Dry 

Lake that affects neighboring lands and elevated salinity levels 

in Lake Bowdoin. Specific concerns are the detrimental effects 

that elevated salinity levels can have on aquatic plants and 

invertebrates that are critical to waterfowl and other waterbirds 

(Gleason and others, 2009). Policies have been enacted to limit 

water (and salt) transfers from Lake Bowdoin to Dry Lake and 

to develop relatively permanent vegetative cover over the Dry 

Lake basin to alleviate some of the blowing salt problems. The 

water-quality issues of Lake Bowdoin have received considerable attention and study (Hamilton and others, 1989; Kendy, 

1999), and management alternatives have been evaluated and 

approved to reduce and maintain salinity levels within an 

acceptable range (U.S. Fish and Wildlife Service, 2011).

Model Inputs

A majority of the data required to run and validate the 

WSB model was available for Lake Bowdoin. A stage-discharge curve was unavailable for Lake Bowdoin; but, because 

the Lake is essentially managed as a closed basin with no outflows, this lack of information did not affect model validation. 

Further, data were not available to account for water exchange 

with Beaver Creek during the 2011 flood described in the following paragraphs.

For 2010, hourly precipitation and temperature were 

obtained from a weather station located at the refuge, and 

solar radiation was obtained at 15-minute intervals from the 

MESOWEST weather station (station MATM) located at 

Malta, Montana (not shown on fig. 3), approximately 7 miles 

(mi) to the west of the refuge (MESOWEST, 2012a). During 2011, hourly precipitation and temperature were obtained 

from a weather station located at the refuge; solar radiation 

was obtained at 15-minute intervals from the Malta weather 

station for the period of May 10–28 and at an hourly interval from the refuge weather station thereafter. Initial conditions for day one of the model runs were set using specific 

conductance and water levels measured in the field during 

data-logger deployment in the spring. Management information such as water-control structure elevations, amounts and 

specific conductance of inflows and outflows, and the surface 

area-capacity-depth curve were obtained from USFWS refuge 

staff. During 2010, the USFWS estimated that 3,485.7 acre-ft 

of water was delivered to Lake Bowdoin from August 23 to 

September 6 (for model validation inputs were calculated in 

equal intervals of 232.4 acre-ft/d); however, data from the 

data loggers indicated that water levels rose steadily from 

August 23 to September 11, so the canal inputs were adjusted 

accordingly by extending the daily inputs (232.4 acre-ft/d) for 

an additional 5 days. There were no managed inputs into the 

lake during 2011.

During 2011 there was significant spring flooding from 

Beaver Creek to Lake Bowdoin that resulted in elevated pool 

elevations and reduced specific conductance levels. The precise duration of the flooding and amount of water exchanged 

are unknown because a large proportion of the water exchange 

took place prior to installation of the data loggers on May 

10. Once the data loggers were installed, a steady increase in 

water levels was observed until about mid-June; there were no 

documented deliveries from the canal during this period and 

the amount of water required to attain the observed pool levels 

greatly exceeded estimated inputs from direct precipitation. A 

comparison between Lake Bowdoin pool elevations and flows 
Approach and Methods 9

from Beaver Creek suggests that a large part of this water 

likely originated from Beaver Creek (fig. 4) because the peak 

flows correspond well to lake pool elevations. Field observations from U.S. Geological Survey (USGS) and USFWS personnel also indicate continued water exchange during this time 

period. Although it would have improved model performance, 

change in water volume was not calculated and included as a 

daily input because of the uncertainty involved. Further, not 

accounting for these ungaged inputs allowed for an assessment 

of model performance during an extreme flood year when 

exchanges between Lake Bowdoin and Beaver Creek typically 

are not quantified. No modifications were made to the WSB 

model, and contributions or losses associated with deflation, 

groundwater, or surface runoff from the surrounding grasslands were not considered.

Long Lake National Wildlife Refuge

LLNWR is located in south-central North Dakota (fig. 5). 

This area is a semiarid (annual precipitation, 15–17 in.) region 

associated with neutral river-flow trends over approximately 

the past 50 years (Anderson and Norton, 2007; Anderson 

and others, 2008). Long Lake, the primary wetland feature 

on the refuge, receives water from Long Lake Creek but also 

receives high spring runoff from local drainages. LLNWR was 

established in 1932 as a refuge for migratory birds and other 

wildlife; currently it provides critical resources for species such 

as cranes, geese, ducks, swans, and shorebirds. The refuge 

is a major staging area for the mid-continent sandhill crane 

(Grus canadensis) population, and threatened piping plovers 

(Charadrius melodus) and endangered whooping cranes (Grus 

americana) regularly utilize refuge habitats. The refuge’s 

importance to the conservation of migratory birds has been recognized by its designation as a Globally Important Bird Area 

and a Western Hemisphere Shorebird Reserve Network site.

Physical Setting

LLNWR encompasses approximately 22,300 acres 

and includes nearly 16,000 acres of lakes and wetlands in a 

grassland and cropland dominated landscape. Long Lake, an 

approximately 16-mi long, 17,000-acre (including nonrefuge 

areas) shallow, alkaline lake is the predominant feature of 

the refuge (fig. 5). Long Lake is divided by dikes and watercontrol structures into four management units. The main body 

of Long Lake consists of Units 1, 2, and 3, which were formed 

by the construction of A, B, and C Dikes during the mid1930s. The fourth unit, Unit 2 marsh, is a roughly 800-acre 

shallow wetland impoundment that was separated from Unit 2 

in 1995 by construction of Unit 2 Marsh Dike and water-control structure (fig. 5). Refuge impoundments are all relatively 

Figure 4. Lake Bowdoin pool elevations and stream discharge (U.S. Geological Survey streamgage 06166000 

Beaver Creek below Guston Coulee near Saco, Montana) from Beaver Creek during 2010 and 2011.

2010 2011

Discharge, in cubic feet per second

0

500

1000

1500

2000

2500

3000

3500,500

0

500

1,000

1,500

2,000

2,500

3,000

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November December 

Month

2,208

2,209

2,210

2,211

2,212

2,213

2,214

Beaver Creek discharge

Lake Bowdoin pool elevation

EXPLANATION

Pool elevation, in feet
10 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Figure 5. Location and primary management units of Long Lake National Wildlife Refuge.

#

##

X

100°16’ 100°08’ 100°00’ 99°52’

46°56’

46°48’

46°40’

NORTH DAKOTA

Study area

Long Lake

National Wildlife Refuge

Lake Sakakawea

Lake Oahe

Long Lake Creek

Unit 2 Marsh

Unit

2

Unit 1

Unit 3

A Dike

B Dike Unit 2 Marsh Dike

C Dike

0 2.25 4.5 9 KILOMETERS

0 2.25 4.5 9 MILES

Long Lake

EXPLANATION

Weather Station

#

X

Data logger

# U.S. Geological Survey

stream gage

Base from Environmental Systems Research Institute, Inc., 2006, various scales 

and Montana Natural Resource Information System, various dates and scales

Universal Transverse Mercator, zone 14N,

Central Meridian -105.0000000

North American Datum of 1983
Approach and Methods 11

shallow with maximum and average water depths less than 

6.5 ft and 3.5 ft, respectively.

Water Resources

The primary water sources for Long Lake are inflows 

from Long Lake Creek, runoff from the contributing drainages around the lake, and direct precipitation. In the semiarid climate of south-central North Dakota, average annual 

evaporation (33–40 in.) exceeds precipitation (16 in.), resulting in a negative ratio between precipitation and evaporation 

(U.S. Fish and Wildlife Service, 2006). Contributions from 

each water source have not been quantified; however, limited 

work performed by the USGS suggests that Long Lake Creek 

supplies approximately 68 percent of the water to Long Lake 

(U.S. Fish and Wildlife Service, 2006). Long Lake Creek 

flows directly into (and out of) Unit 1, which is separated from 

the other units by a dike and water-control structure; therefore, 

water levels in the other impoundments are highly dependent 

on the amount of spring runoff supplied by the contributing 

watersheds around the refuge. Prior to refuge establishment 

and the construction of water-control structures, Long Lake 

likely functioned as a closed-basin, alkaline system during 

average climatic years; water levels would have fluctuated 

dynamically in response to seasonal climatic events. During 

periods of high precipitation, lake levels would rise beyond the 

natural sill, and water would discharge into Long Lake Creek 

downstream from Unit 1 where water exits the refuge (Laubhan and others, 2006). Currently, water flows out of Unit 1 

through the A Dike water-control structure and downstream 

through Long Lake Creek unless lake levels fall below the 

fixed-sill water-control structure at the lake outlet. Losses from 

Units 2 and 3 mainly are attributed to evapotranspiration as 

well as some outflow to Unit 1 (dependent on management). 

In general, direction of water flow in the refuge is from Unit 3 

and Unit 2 into Unit 1 where it exits the refuge. Depending on 

annual and seasonal water inputs (primarily snowmelt runoff) 

and evapoconcentration, a significant salinity gradient can 

develop that increases from Unit 1 to Units 2 and 3.

Management and Environmental Concerns

Prior to the establishment of LLNWR, botulism outbreaks were common and likely resulted in the death of 

hundreds of thousands of birds during severe incidents. In fact, 

one of the primary reasons for constructing the dikes separating Long Lake into management units was to enhance the 

USFWS’s ability to manipulate water levels to combat the outbreaks. However, the USFWS has limited ability to manipulate water levels because Unit 2, Unit 2 marsh, and Unit 3 are 

managed through adjustable water-control structures with a 

limited elevation range, and the water levels for Unit 1 are set 

by a fixed-sill structure. Water levels currently are managed 

primarily to reduce the frequency and magnitude of botulism 

outbreaks to the extent possible and to provide a mosaic of 

habitats, including emergent vegetation, mudflats, and open 

water, to support wetland-dependent birds.

A consequence of constructing the dikes at LLNWR is 

that the full pool elevation of the lake was raised more than 

3 ft. While this increased water-holding capacity may have 

resulted in greater management flexibility, there may be 

unforeseen water-quality consequences associated with altered 

hydrology and prolonged periods of inundation. For example, 

there are concerns that salt concentrations have increased 

because of the interruption of periodic flushing events, and it 

has been suggested that various chemical constituents, such 

as trace metals, may accumulate and reach levels that are 

detrimental to biotic communities (Laubhan and others, 2006). 

As a result, the USFWS has recently implemented a monitoring program to identify potential water-quality (including 

salinity) issues and to broaden and enhance their management 

strategies.

Model Inputs

Only a part of the data required to run and validate the 

WSB model was initially available for LLNWR. The primary 

data gaps were the lack of stage-discharge curves to estimate 

flows from the refuge and exchanges among the management 

units within the refuge. Further, inputs to the refuge from the 

Long Lake Creek watershed were unknown because Long 

Lake Creek does not have an active USGS streamgage station. 

Inputs from the small, ungaged drainages immediately surrounding the refuge were also unknown. These local inflows 

can be significant, especially during spring snowmelt, and can 

account for a large part of the water inputs for Units 2 and 3 

and Unit 2 marsh.

Once these data gaps were identified, additional data collection was initiated with the purpose of developing stage-discharge curves for Long Lake Creek and Unit 1 that could be 

used to estimate overall refuge inflows and outflows associated 

with Long Lake Creek. In cooperation with the USGS North 

Dakota Water Science Center, Acoustic Doppler Velocity 

Meters (ADVMs) were installed in two locations where water 

exits Unit 1 and flows out to Long Lake Creek. Data from the 

ADVMs were used to develop a stage-discharge curve for 

estimating outflow from Unit 1. In addition, limited historic 

data from the inactive USGS streamgage station (USGS 

streamgage 06349215 Long Lake Creek above Long Lake 

near Moffit, N. Dak.) located on Long Lake Creek and streamflow data from an ongoing project with the North Dakota 

Department of Health were used to develop a stage-discharge 

curve for Long Lake Creek. This curve was used in conjunction with elevations from the data logger to estimate inflows to 

the refuge from Long Lake Creek. Accurate estimations of the 

local inflows to Units 2 and 3 and Unit 2 marsh would require 

intensive, long-term study. Therefore, this initial WSB model 

validation was limited to Unit 1.

For 2010 and 2011, hourly data on precipitation, temperature, and solar radiation were obtained from the MESOWEST weather station (station TS633) located at the refuge 

(MESOWEST, 2012b). Specific conductance for inflows 

was obtained from the Long Lake Creek data logger. Initial 
12 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

conditions for day one of the model runs were set using specific conductance and water levels measured in the field during 

data-logger deployment in the spring. Management information such as water-control structure elevations and the surface 

area-capacity-depth curves were obtained from USFWS refuge 

staff.

The outlet for Unit 1 consists of a fixed-sill (nonadjustable) box culvert. The WSB model was modified so that all 

outflow was calculated using the stage-discharge curve developed for Unit 1; if pool elevation drops below the fixed-sill 

elevation then outflow equals zero. The WSB model estimates did not include contributions or losses associated with 

groundwater, surface runoff from the surrounding uplands, or 

bidirectional flows through the water-control structure located 

between Unit 1 and Unit 2.

Sand Lake National Wildlife Refuge

SLNWR is located in northeastern South Dakota (fig. 6). 

This area receives more precipitation (annual precipitation, 

18–20 in.) than the Bowdoin and Long Lake NWRs and is 

associated with a river that has exhibited upward river-flow 

trends over approximately the past 50 years (Anderson and 

Norton, 2007; Anderson and others, 2008). SLNWR is situated 

directly on the James River where two dams form relatively 

large, shallow lakes. SLNWR was established in 1935 as a 

breeding ground and refuge for migratory birds and other 

wildlife. Currently (2013), the NWR supports snow geese 

(Chen caerulescens) and other waterfowl, shorebirds, white 

pelicans (Pelecanus erythrorhynchos), and colonial nesting 

birds; the refuge also is known for the world’s largest nesting 

colony of Franklin’s gulls (Larus pipixcan). Sand Lake has 

been cited as a leading destination for birding and designated a 

Wetland of International Importance and a Globally Important 

Bird Area.

Physical Setting

SLNWR encompasses approximately 21,500 acres, 

including roughly 11,450 acres of wetland habitats. The 

refuge, situated directly on the James River, consists of two 

main water bodies that were created by dams during the 

1930s: Mud Lake and Sand Lake (fig. 6). Mud and Sand 

Lakes cover up to 5,300 and 6,100 acres, respectively, and 

are separated by an earthen dam and water-control structure. 

The James River flows from north to south, and Mud Lake is 

upstream (north) from Sand Lake. Additionally, Sand Lake is 

divided on the north end by a highway with bridges and watercontrol structures that allow water to flow downstream. Both 

impoundments are relatively shallow, with depths averaging 

approximately 1.50 ft in Mud Lake and 2.75 ft in Sand Lake 

during average precipitation years and under current management; maximum pool depths approach 6 ft. Flows through the 

SLNWR are rather slow and barely perceptible.

Water Resources

The primary water sources for Mud and Sand Lakes are 

inflows from the James River and direct precipitation. Flows 

of the James River vary greatly with climate (fig. 7) and water 

levels of Mud and Sand Lakes are highly dependent on spring 

river flows during normal precipitation years. Mud and Sand 

Lakes are considered a flow-through system even though 

water is stored within the refuge impoundments and flow 

through the system is slow.

Management and Environmental Concerns

The standard water-management strategy is to fill Mud 

and Sand Lakes to capacity during the spring and maintain 

full-pool levels through mid-August; levels are dropped in the 

fall to protect infrastructure from ice damage after freezeup. 

Following extended periods of high water (for example, at or 

above full-pool levels), growing-season drawdowns are implemented when conditions permit to facilitate reestablishment 

of emergent vegetation. However, management flexibility is 

limited by infrastructure and flows of the James River.

The primary goal of the refuge staff is to manage Mud 

and Sand Lakes to provide wetland habitats favored by 

overwater-nesting birds and waterfowl. Specific objectives 

include managing the lower part of Mud Lake for 30–50 percent emergent vegetation and the northern end of Sand lake for 

30–60 percent emergent vegetation; water depths ranging from 

approximately 8–20 in. are desirable during spring and summer for both impoundments. Managing wetlands in this manner provides open water in the deeper parts of the lakes and 

shallow water dominated by emergent vegetation along lake 

fringes. This range of habitats supports the overwater-nesting 

birds and waterfowl as well as other wetland-dependent species that prefer the shallow-water habitats.

Because SLNWR is a flow-through system, refuge 

impoundments do not have the same salinity and water-quality 

problems that characterize many of the refuges in the western 

part of the region; however, there are concerns over sedimentation of the Mud Lake impoundment (Gleason and others, 

2003). The primary management concern for refuge staff is 

being able to manage water levels at the desired level, especially during high-flow years when habitats are flooded and 

the dams and water-control structures are overtopped. Consecutive years of high water can result in the loss of emergent 

vegetation habitats that are critical for a large proportion of the 

refuge’s key bird species.

Model Inputs

A majority of the data required to run and validate the 

WSB model were available for SLNWR. Because SLNWR 

is a flow-through refuge situated directly on the river, the 

WSB model required modification to calculate outflows. The 

primary data gap was the lack of stage-discharge curves for 
Approach and Methods 13

Figure 6. Location and primary management units of Sand Lake National Wildlife Refuge.

#

#

#

#

#

#

#

#

X

98°24’ 98°16’ 98°08’ 98°00’

45°52’

45°44’

45°36’

Mud

Lake

Sand Lake

National Wildlife

Refuge

Sand

Lake

Study area

SOUTH DAKOTA

Missouri River

James River

James River

HOUGHTON DAM

COLUMBIA DAM

0 2.25 4.5 9MILES

0 2.25 4.5 9KILOMETERS

EXPLANATION

Weather Station

#

X

Data logger

# U.S. Geological Survey

stream gage

Base from Environmental Systems Research Institute, Inc., 2006, various scales 

and Montana Natural Resource Information System, various dates and scales

Universal Transverse Mercator, zone 14N,

Central Meridian -105.0000000

North American Datum of 1983
14 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

estimating flows from Mud Lake to Sand Lake and from Sand 

Lake to the James River (fig. 6). Additionally, the watercontrol structures and dikes that separate Mud and Sand 

Lakes were overtopped for a part of 2010 and 2011 because 

of extremely high river flows (fig. 7). Therefore, even if the 

appropriate stage-discharge and water-control structure elevation information were available estimating flows would have 

been difficult because discharge exceeded the capacity of the 

water-control structures for extended periods of time.

Because of these limitations, each impoundment could 

not be modeled independently. However, the combined water 

balance of both impoundments was modeled by calculating 

combined areas and volumes. To apply the WSB model in this 

manner, a surface area-capacity-depth relation was developed for both units by summing areas and volumes from the 

individual curves for each impoundment using pool elevation. 

Further, a rough stage-discharge curve was developed based 

on historic pool elevations and stream-discharge rates from the 

USGS streamgage located approximately 3.5 mi downstream 

from the refuge (USGS streamgage 06471000 James River at 

Columbia, S. Dak.); this curve was used to calculate discharge 

from the refuge to the James River. For each date that pool 

elevations and daily discharge (1,397 observations from 1980 

to 2011) were available for both impoundments, a mean pool 

elevation for the refuge (mean of Mud and Sand Lake elevations) was calculated, and this value was related to daily 

discharge. Mean discharge rates were calculated based on 

0.5-ft intervals of pool elevation and a Microsoft Excel lookup 

function was created that estimates daily outflow based on 

elevation. Data were not available to account for water-control 

structure elevation when developing this curve; thus, discharge 

was predicted based solely on pool elevation. There is flow 

from a small local drainage area to the James River that is 

located between the refuge and the USGS streamgage located 

approximately 3.5 mi downstream of the refuge, and the relative volume of this contribution varies seasonally because 

of precipitation events. Therefore, using this streamgage to 

develop the rough stage-discharge curve could result in slight 

overestimates of discharge from the refuge.

For 2010, hourly precipitation and temperature data were 

obtained for the period between May 17 and July 22 from the 

National Oceanic and Atmospheric Administration (NOAA) 

weather station located approximately 3.5 mi to the south of 

the refuge at Columbia, S. Dak. (not shown on fig. 6) (station 

Columbia 8 N; National Oceanic and Atmospheric Administration, 2012). Daily solar radiation for the same period was 

obtained from the North Dakota Agricultural Weather Network 

weather station located approximately 25 mi to the east at 

Britton (not shown on fig. 6), South Dakota (North Dakota 

Agricultural Weather Network, 2012). For the remainder of 

2010 and all of 2011, hourly weather data were obtained from 

a weather station located at the refuge. Inflows to the refuge 

from the James River were estimated using daily discharge 

data from the USGS streamgage located approximately 

3.5 mi above the refuge (USGS streamgage 06470878 James 

River at the North Dakota/South Dakota border) and specific 

Figure 7. Palmer Modified Drought Index values for northeastern South Dakota and discharge for the James 

River (U.S. Geological Survey streamgage 06470878 at the North Dakota/South Dakota border) from October 1, 

1981, to June 1, 2012.

1980 1985 1990 1995 2000 2005 2010 

Year

-8

-6

-4

-2

0

2

4

6

8 8,000

6,000

4,000

2,000

0

Palmer Modified Drought Index (PMDI)

Discharge, in cubic feet per second

PMDI

Discharge

EXPLANATION
Approach and Methods 15

conductance for inflows was obtained from a data logger 

located where the James River enters Mud Lake. Initial conditions for day one of the model runs were set using specific 

conductance and water levels measured in the field during 

data-logger deployment in the spring. Information on management, such as historic pool elevations and surface areacapacity-depth curves was obtained from USFWS refuge staff. 

The WSB model was modified so that estimates of outflow 

were calculated using the stage-discharge curve, regardless of 

water-control structure elevation. Contributions or losses associated with groundwater or surface runoff from the surrounding uplands were not considered.

Model Application

Overview

An overarching goal of USFWS staff at BNWR is to provide and manage wetland habitats for breeding and migratory 

birds and other wildlife. One of the primary management concerns is the long-term accumulation of salts in Lake Bowdoin 

and the resulting increase in salinity that, if not controlled, will 

eventually diminish habitat quality for waterbirds. Evapoconcentration of salts over time can negatively affect aquatic communities such as plants and invertebrates (Gleason and others, 

2009), and elevated salinity can limit management options 

because regulations prohibit downstream releases of water that 

are of lower quality than the receiving waters (for example, 

discharge of saline water from the refuge to Beaver Creek). 

Under current management guidelines there are no regulated 

releases of water from Lake Bowdoin, and the primary mechanisms for salt removal are deflation and infrequent flushing 

events associated with Beaver Creek floods; thus, salts from 

Dodson South Canal and other inflows generally accumulate 

over time.

During development of the CCP (U.S. Fish and Wildlife 

Service, 2011), USFWS personnel evaluated five scenarios for 

managing or removing salts in Lake Bowdoin: (1) current management, (2) evaporation ponds and removal of saline residue, 

(3) natural flushing by Beaver Creek, (4) underground injection 

well and natural flushing by Beaver Creek, and (5) pumping 

to the Milk River. Evaluations of each option were supported 

through assessments of the water and salt balance of Lake 

Bowdoin, and their primary purpose was to identify the best 

alternative for removing salts and maintaining desired salinity levels. Based on these evaluations, the fourth scenario was 

proposed as the best option on the basis of efficacy and cost.

For this study, the WSB model is used in a similar manner to assess effects to Lake Bowdoin associated with a future 

climate scenario, alternative management actions, and natural 

flooding events. The objective was not to duplicate the work 

already performed by the USFWS but to demonstrate the 

utility of the WSB model for simulating habitat characteristics 

and evaluating climatic shifts and alternative management 

objectives. Hence, simulations do not represent actual conditions or proposed management strategies, but show how the 

WSB model could be used to evaluate forecasted climatic 

conditions and management alternatives.

The WSB model was demonstrated using Lake Bowdoin for a number of reasons. Lake Bowdoin is located in a 

semiarid region where salinity problems are common among 

managed wetlands, and there are ample data available because 

the lake has a long history of monitoring and scientific study. 

The refuge is essentially a terminal, closed-basin system 

with regulated canal inputs as the primary water source; thus, 

uncertainty associated with modeling watershed-level processes such as streamflow was reduced. Further, even though 

salts continue to accumulate in refuge wetlands, specific 

conductance oscillates over time in response to water levels 

(concentration and dilution) that can be regulated by management, although control often is limited by the annual allocation 

of water received from the Milk River Project and periodic 

Beaver Creek floods. As an example, figure 8 shows drastic 

reduction in Lake Bowdoin specific conductance levels associated with the two most recent Beaver Creek floods (circa 1986 

and 2011). This figure also shows a moderate relation between 

the occurrence of floods and the Palmer Drought Index (surrogate for climate), and demonstrates that conditions similar to 

those during flood years have occurred numerous times over 

the past century. Therefore, it is important for managers of 

BNWR to have the ability to model habitat conditions while 

considering potential changes to factors that affect the lake’s 

water balance, such as managed inflows, climate, and floods. 

Lastly, high-resolution climate projections (see “Simulated 

Future Climate Inputs” section) for the refuge were available.

Considering the observed and projected trends of accumulating salts and temporal variation in specific conductance 

levels, coupled with projected climate scenarios (Karl and others, 2009; U.S. Fish and Wildlife Service, 2011), logical management questions are “what will Lake Bowdoin water depths 

and specific conductance levels look like under a potential 

future climate, what effects could various management actions 

(for example, altered canal inputs) have on future habitat 

conditions, and what effects could a change in the frequency 

of Beaver Creek floods have on salinity?”

The WSB model was used in conjunction with simulated 

climate data to evaluate effects of climate, management scenarios (altered canal inflows), and the importance of Beaver 

Creek floods on the future water and salt balance and habitat 

characteristics of Lake Bowdoin. Specifically, specific conductance, mean water depth, and inundated and dry surface areas 

were simulated over a 50-year period to address the questions 

posed above. The primary goal of this exercise was to simulate abiotic habitat conditions and to identify potential effects 

to biotic communities. Simulations such as these will allow 

wetland managers to evaluate current or proposed management objectives and strategies and identify where alternatives 

should be developed to address potential shifts in climate 

and water availability. A secondary goal was to demonstrate 

the flexibility of the WSB model for assessing habitat conditions in response to changes in climate, management, or water 

availability.
16 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Methods

Model Simulation

Six 50-year model simulations were performed at a 

daily time step during the approximate ice-free period (April–

November) for Lake Bowdoin. The first simulation was 

intended to assess any effects associated with projected climate 

change; therefore, canal deliveries were based on historical 

averages and held constant among years. The second and third 

simulations were intended to depict changes associated with 

altered canal deliveries. For the second simulation, canal deliveries were reduced by 20 percent to assess the effect of reduced 

salt and water inputs. Conversely, for the third simulation, 

deliveries were increased by 20 percent to assess effects associated with increased salts and dilution through greater canal 

deliveries. A second set of three simulations, similar to those 

described above, were performed to simulate the long-term 

effects of periodic Beaver Creek floods on salinity concentrations. Various assumptions, described in the following paragraph, were made in order to run the WSB model across years; 

therefore, single-season simulations also were performed using 

50-year averages from the climate simulation to remove the 

inherent errors associated with these assumptions.

For the first set of simulations, water balance information for the winter months (December–March) was estimated 

based on the historic average, and this value was used to set 

initial conditions at the beginning of the active model period 

(April 1) of each year (see “Model Inputs” section). For 

example, the long-term average snowmelt-runoff volume was 

included on the first active model day of each year. Initial 

conditions (specific conductance, pool elevation) for the first 

year of all simulations were arbitrarily specified as a mean of 

the observed values from August 2011. The first set of three 

simulations did not include any inputs from Beaver Creek 

(periodic floods). The second set of three simulations included 

substantial Beaver Creek floods at a 20-year frequency of 

occurrence. It is difficult to predict the timing or magnitude of 

these flood events, but frequency and exchange volume were 

approximated based on existing data and past events (fig. 8). 

For all simulations, the lake was assumed to be a terminal, 

closed-basin system by setting the water-control structure 

elevation at the maximum of 2,214 ft.

Model Inputs

Daily temperature and precipitation values were obtained 

from a simulation of the A2 emissions scenario (see “Simulated 

Future Climate Inputs” section). Daily evapotranspiration was 

estimated using the Jensen-Haise model along with daily temperature and solar radiation; daily solar radiation was based on 

a 10-year daily average (2000–10) for Malta, Mont. Temperature and precipitation were the only daily input variables that 

differed among years, all other variables remained unchanged. 

The timing and amount of water deliveries from the Dodson 

South Canal were calculated based on estimated deliveries 

from 1988 to 2008; daily values were calculated by dividing 

the mean monthly value by the number of days in the month. 

Figure 8. Palmer Modified Drought Index values (1895–2012) for north-central Montana and mean monthly 

specific conductance (1975–2011) for Lake Bowdoin. Arrows approximate the two most recent Beaver Creek 

flooding events (circa 1986, 2011). Palmer Modified Drought Index (PMDI)

-10

-8

-6

-4

-2

0

2

4

6

8

10

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 

0

60,000

48,000

36,000

24,000

12,000

Specific conductance, in microsiemens per centimeter at 25 degrees Celsius

PMDI

Specific conductance

EXPLANATION

Beaver Creek flood

Year
Approach and Methods 17

Specific conductance of the canal deliveries was based on 

existing data (mean from 1987 to 2007) and set at 600 μS/cm.

Simulations are constrained by uncertainties associated 

with the choice of starting conditions, annual canal deliveries (timing and amount), estimates of ET and spring runoff 

(including floods), and precipitation and temperature from 

the modeled climate data. The WSB model was designed to 

run for a single ice-free season. Multiyear runs are difficult to 

implement because snowpack, timing and volume of spring 

runoff, and wintertime evaporative losses are extremely variable and difficult to accurately estimate. Consequently, contributions and losses were estimated over the winter months 

to conduct the 50-year simulations, and this information was 

used to set initial conditions on April 1 of each year. Losses to 

sublimation were applied at a rate of 1inch per month (Kendy, 

1999). To account for inputs from winter precipitation and 

spring snowmelt, mean change in surface-water elevation 

was determined from fall to spring over a 17-year period (fall 

of 1990–spring of 2007); volume of water required for this 

change was calculated using the surface area-capacity-depth 

curve. Based on these calculations, 1,105 acre-ft of water (specific conductance = 100 μS/cm) were added on the first model 

day (April 1) of each year to account for winter precipitation 

and spring runoff. For the simulations that included Beaver 

Creek floods, water volume of Lake Bowdoin before and after 

the 2011 flood was approximated using measured pool elevation and the surface area-capacity-depth curve. The change in 

volume, which was approximately 13,760 acre-ft, was attributed to flooding from Beaver Creek; hence, this volume was 

applied on the first model day (April 1) for each of the 2 years 

where floods were simulated.

Simulated Future Climate Inputs

A regional climate simulation was performed for water 

years 2001–50 (Norton and Stamm, 2012); data from the two 

grid points that overlay BNWR were used for this modeling 

exercise. Climate output is from the Weather Research and 

Forecasting (WRF) model (Skamarock and others, 2008), 

which is a dynamical, high-resolution model. Initial and 

boundary condition data were from the Community Climate 

Systems Model (version 3.0) simulation of the A2 emissions 

scenario (Nakićenović and Swart, 2000). Overall, the 50-year 

simulation predicts a slight upward trend in mean annual and 

seasonal (April–November simulation period) temperature. 

This trend exceeds the recent 10-year (2001–11) annual average of 43.7 °F for Malta, Mont., in most instances (fig. 9A.). 

Simulated annual and seasonal precipitation, however, is 

highly variable with no obvious trends (fig. 9B). Simulated 

annual precipitation exceeds the area’s 12-in. annual average 

(U.S. Fish and Wildlife Service, 2011) in greater than approximately 80 percent of the simulation years. On the basis of this 

climate simulation, there is potential for higher rates of water 

loss through ET because of higher temperatures, and greater 

than average water inputs through precipitation for a great 

majority of the simulation years.

Figure 9. Outputs from the Weather Research and Forecasting 

(WRF) model simulation. A, Mean temperature for the entire 

calendar year (annual) and for the April to November time period 

(simulation period) used in the Lake Bowdoin simulation. B, Total 

precipitation for the entire calendar year (annual) and for the 

April to November time period (simulation period) used in the Lake 

Bowdoin simulation.

Annual

Simulation period

Annual mean (2001–11; Malta, Mont.)

EXPLANATION

Precipitation, in inches Temperature, in degrees Fahrenheit

2000 2010 2020 2030 2040 2050

Year

35

40

45

50

55

60

65

0

5

10

15

20

25

30

2000 2010 2020 2030 2040 2050

Year

B

A
18 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Validation and Application of the 

Water and Salt Balance Model

Results of Model Validation

Bowdoin National Wildlife Refuge

In general, the WSB model produced temporal patterns 

and trends of pool elevation and specific conductance that 

were similar to measured values (fig. 10, table 1). The mean 

daily absolute differences between modeled and measured 

pool elevation were 0.06 ft for 2010 and 0.38 ft for 2011. 

These differences equated to approximately 1.8 percent and 

7.8 percent of the mean modeled water depths for 2010 and 

2011, respectively. Mean daily absolute differences between 

modeled and measured specific conductance levels were 

415.9 μS/cm (2.9 percent of observed mean) and 936.2 μS/cm 

(12.1 percent of observed mean) for 2010 and 2011, respectively. The WSB model consistently predicted higher specific 

conductance levels and underpredicted peak pool elevations 

during 2011. These discrepancies likely were a result of significant inputs of freshwater from the 2011 Beaver Creek flood 

(fig. 4) that resulted in higher observed water levels and lower 

observed specific conductance values when compared to the 

modeled values. The model also provided estimates of mean 

water depth and surface areas (fig. 11) that are calculated using 

the surface area-capacity-depth curve; the precision of these 

estimates was not assessed.

Overall, WSB model performance was superior during 2010 when there was no unmanaged mixing with Beaver Creek; however, despite the fact that water inputs from 

the 2011 spring flooding were not included, the model still 

reflected pool elevations and specific conductance levels 

adequate for management (fig. 10). Disregarding the obvious 

unmanaged inputs during the spring of 2011, the WSB model 

predicted a lower rate of decline in pool elevation after midJune when compared to the observed trend. This observation 

suggests there were unmanaged (ungaged) outflows because 

of high water levels or actual ET was greater than predicted. 

Because the WSB model (estimated ET) seemed to perform 

well throughout 2010, the divergence between the modeled 

and measured rate of decline during 2011 was likely due to 

unmanaged outflows not accounted for in the model. However, 

the possibility that a part of this discrepancy is due to differences between modeled and actual ET cannot be discounted.

Modeled elevation

Measured elevation

Modeled specific conductance

Measured specific conductance

EXPLANATION

2,209

2,208

2,211

2,210

2,213

2,212

2,214

Month

April

May

June

July

August

September

October

NovemberDecember

January

February

March

April

May

June

July

August

September

October

November

December

Pool elevation, in feet

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

2010 2011

Specific conductance, in microsiemens per centimeter at 25 degrees Celsius

Figure 10. Modeled and measured pool elevation and specific conductance for Lake Bowdoin from May 14 to 

November 9, 2010, and May 10 to October 25, 2011.
Validation and Application of the Water and Salt Balance Model 19

Figure 11. Modeled mean water depth and surface areas (inundated, dry) for Lake Bowdoin from May 14 to 

November 9, 2010, and May 10 to October 25, 2011.

Table 1. Summary statistics comparing measured values to the 2010 and 2011 model simulations of Bowdoin, Long Lake, and Sand 

Lake National Wildlife Refuges.

[Annual mean, median, and maximum differences (absolute and percent) are presented for pool elevation and specific conductance. Absolute values are differences between modeled and measured pool elevation and specific conductance. Percentages were calculated using the absolute differences and measured and 

modeled values for specific conductance and pool elevation, respectively. μS/cm, microsiemens per centimeter at 25 degrees Celsius]

Year Days

Pool elevation Specific conductance

Absolute difference, feet Percent difference Absolute difference, μS/cm Percent difference

Mean Median Maximum Mean Median Maximum Mean Median Maximum Mean Median Maximum

Bowdoin National Wildlife Refuge

2010 180 0.06 0.05 0.26 1.8 1.62 7.55 415.9 351.37 1,874.17 2.9 2.62 12.00

2011 169 0.38 0.38 1.03 7.8 8.04 18.40 936.2 932.68 1,659.82 12.1 11.24 20.23

Long Lake National Wildlife Refuge

2010 211 0.27 0.29 0.99 4.2 4.41 15.77 116.0 91.81 449.97 8.2 6.91 29.93

2011 169 0.33 0.34 0.60 4.7 4.83 8.64 188.6 149.37 439.45 16.8 12.29 39.48

Sand Lake National Wildlife Refuge

2010 164 0.81 0.38 2.04 8.6 3.48 22.67 90.9 65.71 351.62 9.0 7.20 31.20

2011 169 0.43 0.48 0.74 3.4 3.83 5.76 47.9 35.28 107.90 5.1 3.84 11.42

Depth

Surface area, inundated

Surface area, dry

EXPLANATION

0

2

4

6

8

10

2010 2011

April

May

June

July

August

September

October

November

December

January

February

March

April

May

June

July

August

September

October

November

December

5,000

4,000

3,000

2,000

1,000

0

Mean depth, in feet

Surface area, in acres

Month
20 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Long Lake National Wildlife Refuge

In general, the WSB model produced temporal patterns 

and trends of pool elevation and specific conductance that 

were similar to measured values (fig. 12, table 1). The mean 

daily absolute differences between modeled and measured 

pool elevation were 0.27 ft for 2010 and 0.33 ft for 2011. 

These differences equated to approximately 4.2 percent and 

4.7 percent of the mean modeled water depths for 2010 and 

2011, respectively. Mean daily absolute differences between 

modeled and measured specific conductance levels were 

116.0 μS/cm (8.2 percent of observed mean) and 188.6 μS/cm 

(16.8 percent of observed mean) for 2010 and 2011, respectively. The model also provided estimates of mean water depth 

and surface areas (fig. 13) that are calculated using the surface 

area-capacity-depth curve; the precision of these estimates was 

not assessed.

Modeled mean pool elevations from the WSB model 

were, on average, within 0.33 ft of measured values (fig. 12) 

despite the fact that water exchanges were not accounted for 

between Units 1 and 2; however, water levels were fairly 

consistent among Units 1 and 2 and flows were likely minimal. Overall, modeled elevation was consistently lower than 

measured elevation. Modeled specific conductance mimicked 

the overall observed seasonal trend during 2010 with greater 

divergence between estimated and measured values when 

specific conductance changed abruptly. During 2011, modeled 

specific conductance was more similar to measured values 

during the first part of the year, with greater divergence evident after the water levels began to drop steadily (fig. 12). The 

WSB model performance likely could be enhanced by increasing the accuracy of the stage-discharge curves, refining the 

relatively coarse surface area-capacity-depth curve, and developing a method to estimate water exchanges between Unit 1 

and Unit 2. Further, expanding the WSB model to include Unit 

2, Unit 3, and Unit 2 marsh will require monitoring to quantify 

flows between all units and to estimate contributions from the 

local drainages.

Sand Lake National Wildlife Refuge

In general, the WSB model produced temporal patterns 

and trends of pool elevation and specific conductance that 

were similar to measured (mean for Mud and Sand Lake) 

values (fig. 14, table 1). The mean daily absolute differences 

between modeled and measured pool elevation were 0.81 ft Specific conductance, in microsiemens per centimeter at 25 degrees Celsius

Pool elevation, in feet

2,500

2,000

1,500

1,000

500

0

April

May

June

July

August

September

October

NovemberDecember

January

February

March

April

May

June

July

August

September

October

NovemberDecember

Month

EXPLANATION

Modeled elevation

Measured elevation

Modeled specific conductance

Measured specific conductance

1,720

1,716

1,717

1,718

1,719

1,715

2010 2011

Figure 12. Modeled and measured pool elevation and specific conductance for Unit 1 of Long Lake National 

Wildlife Refuge from April 23 to November 19, 2010, and May 11 to October 26, 2011.
Validation and Application of the Water and Salt Balance Model 21

for 2010 and 0.43 ft. for 2011. These differences equated to 

approximately 8.6 percent and 3.4 percent of the mean modeled water depths for 2010 and 2011, respectively. Mean daily 

absolute differences between modeled and measured specific 

conductance levels were 90.9 μS/cm (9.0 percent of observed 

mean) and 47.9 μS/cm (5.1 percent of observed mean) for 

2010 and 2011, respectively. The model also provided estimates of mean water depth and surface areas (fig. 15) that are 

calculated using the surface area-capacity-depth curve; the 

precision of these estimates was not assessed.

Overall, modeled specific conductance was very close 

to the measured values for both years (fig. 14). However, this 

is not surprising since Mud and Sand Lakes are freshwater 

flow-through systems with little seasonal variation in specific 

conductance. The WSB model also predicted mean pool elevation fairly well, although there was greater deviation between 

modeled and measured elevations during the fall of 2010 and 

spring and fall of 2011 (fig. 14). Despite this variation, the 

WSB model performance exceeded expectations given the 

data limitations. The WSB model performance likely would 

improve if sufficient data were available to develop more 

accurate stage-discharge curves.

Discussion of Model Validation

The WSB model was adapted to three NWRs, and modeled and measured trends were compared over the approximate ice-free parts of 2010 and 2011. Site-specific model 

input data and management information were used, and no 

model adjustments or calibrations were applied to improve 

simulation results. Modeled pool elevation and specific 

conductance values were, on average, within approximately 

9 and 17 percent of reference values, respectively, based on 

absolute daily differences (figs. 10, 12, 14; table 1). Annual 

Figure 13. Modeled mean water depth and surface areas (inundated, dry) for Unit 1 of Long Lake National 

Wildlife Refuge from April 23 to November 19, 2010, and May 11 to October 26, 2011.

Depth

Surface area, inundated

Surface area, dry

EXPLANATION

Surface area, in acres

0

400

800

1,200

1,600

2,000

2010 2011

0

2

4

6

8

10

Mean depth, in feet

April

May

June

July

August

September

October

NovemberDecember

January

February

March

April

May

June

July

August

September

October

NovemberDecember

Month
22 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

average differences between modeled and measured specific 

conductance ranged from 48–936 μS/cm (table 1). On the 

basis of relations between biotic communities and specific 

conductance (Gleason and others, 2009), these differences are 

small enough, in most cases, to not greatly affect ecological 

interpretation.

Modeled temporal trends were reasonably similar to measured trends when model input data were relatively complete; 

however, there were deviations among the modeled and measured trends when data were missing or when the model relied 

on relatively imprecise stage-discharge or surface-area-capacity curves. For example, the model produced temporal trends 

that were very similar to measured trends for Lake Bowdoin 

during 2010 when the input data were complete; modeled data 

showed divergence from measured trends during 2011 when 

estimates of water exchange with Beaver Creek were unavailable (fig. 10).

On the basis of these comparisons, the WSB model is 

capable of simulating the overall water and salt balance for 

managed wetland impoundments and can be used as a tool 

to evaluate habitat conditions associated with climate scenarios, management actions, or changes to water availability. 

Moreover, the successful application of the WSB model to a 

diversity of impoundments associated with varying data quality and availability demonstrated the model’s flexibility and 

adaptive structure. As an example, the WSB model, which was 

unmodified for Lake Bowdoin, calculates surface outflow on 

the basis of water-control structure elevation. For application 

to LLNWR and SLNWR, the model was modified to calculate 

outflow using a stage-discharge curve.

The performance of the WSB model validates the decision to simplify the original BNWR model (Hamilton and 

others, 1989) to account for only the primary sources of water 

and salts. If some of the secondary sources (for example, 

groundwater) had a large effect, at least in the short term, the 

WSB model would not have predicted trends as well as it 

did. However, small amounts of salts contributed by secondary sources can accumulate over time and eventually have 

a significant impact. Further, direct surface runoff would 

be considered a primary water source if model simulations 

Modeled elevation

Measured elevation

Modeled specific conductance

Measured specific conductance

EXPLANATION

1,294

1,292

1,290

1,288

1,286

1,284 0

1,000

2,000

3,000

4,000

5,000

Pool elevation, in feet

2010 2011

Specific conductance, in microsiemens per centimeter at 25 degrees Celsius

April

May

June

July

August

September

October

NovemberDecember

January

February

March

April

May

June

July

August

September

October

November

December

Month

Figure 14. Modeled and measured pool elevation and specific conductance for Sand Lake National Wildlife 

Refuge from May 17 to November 22, 2010, and May 12 to October 27, 2011. Pool elevations and specific 

conductance values represent a mean for Mud and Sand Lakes. Gaps in the measured pool elevation and 

specific conductance data during 2010 are for periods where data were not available.
Validation and Application of the Water and Salt Balance Model 23

had been performed across periods that included snowmelt; 

however, the WSB model is structured so that additional data, 

such as snowmelt runoff, can be easily incorporated. For the 

WSB model, direct surface runoff attributed to overland flow 

was not included because most impoundments on NWRs in 

the region are surrounded by relatively low-relief grasslands, 

dikes, and elevated roadbeds; therefore, the potential for large 

amounts of direct surface runoff from precipitation generally 

is low.

The simple WSB model simulated the overall water and 

salt balance of managed impoundments, on average, within 

17 percent of measured values (table 1). Model performance 

for a given impoundment, however, could be improved with 

more accurate calculations of variables such as surface area, 

volume, depth, and discharge. As an example, more precise 

surface area-capacity-depth curves, and stage-discharge curves 

developed for a range of water-control structure elevations, 

could greatly improve, in many instances, model performance. 

Similarly, the ability to accurately predict inputs from local 

drainages, which often contribute significant amounts of 

water to refuge impoundments, would be extremely beneficial. Further, the WSB model provides only rough estimates 

of surface areas (inundated, dry) and a mean depth for the 

impoundment. Incorporation of the WSB model into a spatial 

geographic information system (GIS) framework, in conjunction with high-resolution bathymetry data, would provide a 

more detailed description of habitat characteristics by depicting variables such as water depth or surface area of mud flats 

in a spatially-explicit manner.

Results of Model Application to Bowdoin 

National Wildlife Refuge

Simulation Results

Results from the three 50-year and three single-year 

simulations are presented graphically for BNWR. The black 

lines represent simulations based on the WRF climate projections and average canal inputs from previous years (climate 

Figure 15. Modeled mean water depth and surface areas (inundated, dry) for Sand Lake National Wildlife 

Refuge from May 17 to November 22, 2010, and May 12 to October 27, 2011. Values were modeled using the 

combined surface area-capacity-depth curve for Mud and Sand Lakes.

Depth

Surface area, inundated

Surface area, dry

EXPLANATION

Mean depth, in feet

25,000

20,000

15,000

10,000

5,000

0

Surface area, in acres

0

3

6

9

12

15

2010 2011

April

May

June

July

August

September

October

NovemberDecember

January

February

March

April

May

June

July

August

September

October

November

December

Month
24 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

simulation) for figures 16–20. The remaining lines represent 

simulations based on the climate projections and modifications 

to the average canal deliveries (management simulations); 

blue and green lines represent 80 and 120 percent of the average canal deliveries, respectively.

The 50-year climate simulation of Lake Bowdoin (black 

line in fig. 16) showed an initial increase in water depth, 

which approached the maximum depth within approximately 

10 years. Water depth fluctuated but remained relatively stable 

thereafter (fig. 16A). The simulation predicted an overall 

reduction in specific conductance levels, primarily owing to 

salt losses through surface flows (fig. 16B). Mean annual specific conductance decreased from 7,138 to 2,434 μS/cm over 

the simulation period, a decrease of approximately 66 percent. 

Similar to depth, the simulation showed that the inundated 

and dry surface areas consistently approached the maximum 

and minimum levels, respectively (fig. 16C). The mass of salts 

declined greatly over the simulation period, with a decrease in 

the mean annual mass of approximately 73,000 tons over the 

simulation period (fig. 16D).

The 50-year management simulations of Lake Bowdoin 

(fig. 16) resulted in water depths and surface areas that were 

comparable to the climate scenario (fig. 16A, 16C). Overall, 

depths for the 80-percent scenario were slightly lower compared to the average scenario while depths from the 120-percent scenario were slightly greater than the average scenario. 

Inundated and dry surface areas corresponded to the changes 

in depth. Trends in specific conductance and mass of salts 

also were similar among the climate and management scenarios, but the magnitude of change varied over the simulation 

period (fig. 16B, 16D). The 80-percent scenario resulted in 

the highest specific conductance levels while the 120-percent scenario resulted in the lowest. The variation in specific 

conductance among the scenarios was primarily because of the 

greater loss of salts through surface outflow associated with 

the higher inflow scenarios (100 and 120 percent). Although 

the increased-delivery scenario resulted in more imported 

salts than the reduced-delivery scenario, greater water losses 

resulted in a nearly 78,000 ton difference in the mass of salts 

between the two management simulations (fig. 16D).

Overall, relations among the three scenarios were similar 

between the single-year and 50-year simulations (figs. 16, 17). 

The exception was mass of salts, which showed opposing patterns among the management scenarios (figs. 16D, 17D). The 

80-percent scenario resulted in the greatest mass of salts for 

the 50-year simulation, while the 120-percent scenario resulted 

in the greatest mass for the single-year simulation. These 

simulations differed with respect to salt mass because pool 

elevation did not exceed the water-control structure elevation 

during the single-year simulation; thus, there were no surface 

outflows that resulted in the loss of salts. Additionally, the 

overall magnitude of changes from the beginning to the end 

of the simulations, especially for specific conductance and 

mass of salt, were much smaller for the single-season simulations because of the shorter timeframe. However, if these 

small changes were extrapolated over time, they could become 

significant.

The single-year simulations displayed patterns in all 

variables that were associated primarily with seasonal precipitation, ET, and canal deliveries (fig. 17). Water depth remained 

constant until approximately June when water levels declined 

because ET exceeded water inputs. Water levels increased 

during late summer and fall because of increased canal inputs, 

primarily in September (fig 17A). Patterns in surface areas 

corresponded to changes in depth (fig. 17C). Similarly, specific conductance displayed a seasonal trend associated with 

concentration and dilution effects as water levels declined 

and rose (17B). Although the 120-percent delivery scenario 

resulted in the greatest mass of salt, it displayed the lowest specific conductance because of dilution associated with 

higher water inputs.

The 50-year simulations (climate and management) of 

Lake Bowdoin that included 2020 and 2040 Beaver Creek 

flood events showed similar relations among the three scenarios as those that did not include floods (figs. 16, 18). The 

simulated floods, however, did result in greater losses of salts 

to outflow and lower specific conductance levels when compared to the nonflood simulations (figs. 16B, 16D, 18B, 18D). 

Further, the simulated floods resulted in noticeable decreases 

in specific conductance levels because of the removal of salts 

and dilution effects (figs. 18B, 18D). Differences in water 

depths between the flood and nonflood simulations were 

minimal because pool elevations remained near the maximum 

level, and water was lost to surface flow when this level was 

exceeded.

Discussion of Model Application

Results from the Lake Bowdoin simulations (figs. 16–18) 

suggest that the climate and management scenarios would 

result in near-maximum water depths and reduced specific 

conductance levels compared to recent observed conditions 

(figs. 4, 8). These model simulations demonstrate how a future 

climate characterized by above-average precipitation (fig. 9), 

compared to past and current observations, could have major 

impacts to an impoundment by increasing and stabilizing 

water levels and reducing salinity levels. The simulations 

also demonstrate the importance of management in terms of 

affecting habitat characteristics such as salinity and depth 

(fig. 16). Managers can manipulate depth and salinity levels 

of a closed-basin system in numerous ways. For example, the 

mass of salts could be decreased by limiting salt inputs associated with managed water inputs, but if water volumes also are 

decreased, specific conductance values may increase. Conversely, increasing water inputs (or lowering the water-control 

structure elevation) could result in a significant export of salts 

through surface flow, and the remaining salts could be diluted 

by the greater volume of water. In reality, when making management decisions, USFWS personnel must simultaneously 

consider all components that affect an impoundment’s water 
Validation and Application of the Water and Salt Balance Model 25

Figure 16. Results from the 50-year model simulations of Lake Bowdoin. A, Mean water depth; B, Specific conductance; C, Inundated 

and dry surface areas; and D, Mass of salts.

0

2

4

6

8

Depth, in feet

2000 2010 2020 2030 2040 2050 

Specific conductance, in microsiemens per centimeter 

at 25 degrees Celsius

0

2,000

4,000

6,000

8,000

2000 2010 2020 2030 2040 2050 

Year Year

2.0e+4

4.0e+4

6.0e+4

8.0e+4

1.0e+5

1.2e+5

1.4e+5

1.6e+5

Dry

Inundated

Mass, in tons

Year Year

2000 2010 2020 2030 2040 2050 2000 2010 2020 2030 2040 2050 

5,000

4,000

3,000

2,000

1,000

0

Surface area, in acres

A

C

B

D

EXPLANATION

Average canal deliveries

80 percent of average canal deliveries

120 percent of average canal deliveries
26 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Figure 17. Results from the single-year model simulations of Lake Bowdoin. A, Mean water depth; B, Specific conductance; C, 

Inundated and dry surface areas; and D, Mass of salts. Depth, in feet Surface area, in acres

A B

C D

0

1

2

3

4

5

April 

May 

June 

July 

August 

September 

October 

November December 

April 

May 

June 

July 

August 

September 

October 

November December 

Month Month

April 

May 

June 

July 

August 

September 

October 

November December 

April 

May 

June 

July 

August 

September 

October 

November December 

Month Month

10,000

8,000

6,000

4,000

2,000

0

1.30e+5

1.31e+5

1.32e+5

1.33e+5

1.34e+5

1.35e+5

Specific conductance, in microsiemens per centimeter 

at 25 degrees Celsius

Mass, in tons

Dry

Inundated

Average canal deliveries

80 percent of average canal deliveries

120 percent of average canal deliveries

EXPLANATION

0

2,000

2,000

3,000

4,000

5,000
Validation and Application of the Water and Salt Balance Model 27

Figure 18. Results from the 50-year model simulations of Lake Bowdoin that included Beaver Creek floods. A, Mean water depth; B, 

Specific conductance; C, Inundated and dry surface areas; and D, Mass of salts.

Year

2000 2010 2020 2030 2040 2050 

Depth, in feet

0

2

4

6

8

Year

2000 2010 2020 2030 2040 2050 

Specific conductance, in microsiemens per centimeter

at 25 degrees Celsius

Year

2000 2010 2020 2030 2040 2050 

Surface area, in acres

Year

2000 2010 2020 2030 2040 2050 

Mass, in tons

0

2.0e+4

4.0e+4

6.0e+4

8.0e+4

1.0e+5

1.2e+5

1.4e+5

1.6e+5

C D

5,000

4,000

3,000

2,000

1,000

0

0

2,000

4,000

6,000

8,000

Dry

Inundated

A B

Average canal deliveries

80 percent of average canal deliveries

120 percent of average canal deliveries

EXPLANATION
28 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Figure 20. Specific conductance from the 50-year model simulations of Lake Bowdoin that included Beaver Creek floods 

overlain with salinity category boundaries.

0

10,000

20,000

30,000

40,000

50,000

2000 2010 2020 2030 2040 2050 

Year

Specific conductance, in microsiemens per centimeter

at 25 degrees Celsius

Fresh

Slightly brackish

Moderately brackish

Brackish

Subsaline

Saline

Average canal deliveries

80 percent of average canal deliveries

120 percent of average canal deliveries

Salinity category boundaries

EXPLANATION

Figure 19. Specific conductance from the 50-year model simulations of Lake Bowdoin overlain with salinity category 

boundaries.

Fresh

Slightly brackish

Moderately brackish

Brackish

Subsaline

Saline

2000 2010 2020 2030 2040 2050 

Year

0

10,000

20,000

30,000

40,000

50,000

Specific conductance, in microsiemens per centimeter 

at 25 degrees Celsius

Average canal deliveries

80 percent of average canal deliveries

120 percent of average canal deliveries

Salinity category boundaries

EXPLANATION
Summary and Conclusions 29

balance, as well as factors such as biological goals and the 

availability of water for management.

Simulation results also demonstrate the importance of 

periodic Beaver Creek floods to regulating salinity levels of 

Lake. The flood simulations included two floods events, both 

of which noticeably reduced specific conductance and mass 

of salts (fig. 18). The abrupt changes in specific conductance 

associated with the simulated floods corresponded well to the 

observed changes associated with the two most recent Beaver 

Creek floods (fig. 8). These simulations, along with the past 

observations, demonstrate how natural events such as floods 

can play an important role in maintaining salinity levels over 

time by periodically flushing and diluting salts.

The example application of the WSB model to Lake 

Bowdoin demonstrated its utility for depicting various habitat 

characteristics in response to changes in factors that affect an 

impoundment’s water balance. However, model results must 

be related to biological goals and objectives to support the 

USFWS’s conservation-oriented management. Lake Bowdoin 

simulation results are discussed in the following text in terms 

of their implications to biotic communities of the lake.

Gleason and others (2009) presented the mean annual 

specific conductance levels for Lake Bowdoin from 1975–

2007 along with wetland salinity categories (Stewart and 

Kantrud, 1972) that ranged from fresh to saline. These data 

showed that Lake Bowdoin typically falls within the brackish 

category but oscillates from moderately brackish to subsaline 

in response to concentration (for example, pool drawdown 

because of drought) and dilution (for example, Beaver Creek 

floods) episodes.

Gleason and others (2009) also performed a literature 

review and used the resulting data to depict the optimal salinity levels for common aquatic plant and invertebrate taxa. 

Results from this review indicate that most taxa are found in 

waters classified as moderately brackish (less than 5,000 μS/

cm) or fresher, and that taxon diversity is reduced when salinity levels approach or exceed subsaline (greater than 15,000 

μS/cm). Thus, an obvious management objective would be 

to maintain salinity levels in the fresh to moderately brackish range. In the case of Lake Bowdoin, moderately brackish 

waters would be an appropriate target because the lake is 

naturally brackish, and this would be within the normal range 

of variation for this geographic location. When the Stewart 

and Kantrud (1972) salinity categories are superimposed on 

model results for specific conductance (figs. 19–20) inferences 

pertaining to the effects of climate, management, and flood 

scenarios on the biotic communities of Lake Bowdoin can be 

made.

On the basis of these straightforward comparisons, it is 

evident all simulations resulted in relatively stable salinity 

levels ranging from slightly brackish to brackish (figs. 19–20); 

thus, the conditions that these simulations were founded on 

would result in habitat characteristics favorable for most 

aquatic plants and invertebrates currently inhabiting the lake 

(Gleason and others, 2009). It is important to note, however, 

that model scenarios were based on various assumptions such 

as consistent canal deliveries and management among years 

and relied on modeled climate data based on a single emission 

scenario. Further, no guidance was provided by wetland managers pertaining to any proposed management plans. Thus, 

results are not meant to guide management; rather, the simulations are a demonstration of the WSB model’s utility.

In summary, various model simulations of Lake Bowdoin were performed with the purpose of demonstrating how 

the WSB model can be used as a management tool. In doing 

so, potential habitat characteristics were depicted based on a 

future climate scenario and the results demonstrated how two 

opposing management actions and natural flood events may 

affect these characteristics. Simulations such as these will 

allow wetland managers to assess potential effects to various 

habitat metrics from changes to climate and water availability, 

or alternative management objectives or strategies. Although 

simulations were limited by various assumptions and constrained by several simulation parameters (for example, A2 

climate scenario), results demonstrated potential effects of 

a wetter and warmer climate, management (water and salt 

deliveries), and natural floods to the water and salt balance of 

Lake Bowdoin.

Summary and Conclusions

The water and salt balance (WSB) model was described 

and validated using three geographically distinct National 

Wildlife Refuges (NWRs) with unique data limitations and 

differing relations to water resources associated with rivers. 

Overall, the WSB model simulated temporal trends in specific 

conductance and pool elevation (depth) that were comparable to measured trends over the 2-year simulation period. 

However, model accuracy and the magnitude of differences 

between modeled and observed values varied seasonally and 

among refuges. Model performance would be expected to 

improve by addressing various data limitations relating to factors such as water inputs and losses, impoundment bathymetry, 

and water discharge rates. Further, application of site-specific 

calibrations or adjustments likely would improve model 

performance.

Simulations of Lake Bowdoin demonstrated how the 

WSB model can be used as a management tool for assessing 

various habitat characteristics in light of long-term changes 

to climate and water availability and alternative management 

actions. This exercise also highlighted the importance of longterm monitoring and data collection to facilitate development 

of model simulations and to support biological interpretations 

of results.

The water balance of managed impoundments associated with rivers can be affected in various ways by climate, 

water availability, and management. The WSB model allows 

for predictions of habitat conditions based on water inputs, 

losses, and management. This type of model can be very 

effective when applied to closed-basin systems with an 
30 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

indirect connection to a river (for example, Lake Bowdoin) 

because riverine inputs are regulated by wetland managers, 

and estimates of actual streamflow are not required to evaluate 

management scenarios. Conversely, “in-stream” refuges with 

direct connections to rivers (for example, Sand Lake NWR) 

have more limited management capabilities, and any modeling 

efforts would be highly dependent on streamflow estimates for 

inputs.

One approach to conduct scenario-based modeling for 

these flow-through type of systems would be to use historic 

streamflow data associated with specific climatic periods (for 

example, extreme wet/dry periods) that emulate anticipated 

climate conditions to evaluate proposed future management 

actions across a range of observed conditions. For example, 

figure 7 shows streamflow for the James River and Palmer 

Modified Drought Index (PMDI) values from 1981–2012. This 

figure demonstrates the relation between overall moisture patterns (PMDI) and river flows and could be used to identify a 

range of conditions for modeling exercises. Another approach, 

which would be especially desirable when evaluating potential climate change, would be to model streamflow stratified 

by specific conditions such as increased temperatures, earlier 

snowmelt, and decreased precipitation. However, streamflow 

is dependent not only on weather patterns but on runoff and 

water management upstream in the watershed. Processes such 

as reservoir management and watershed runoff are complex 

and difficult to predict and model, which limits the ability of 

the model to comprehensively evaluate the effects of predicted climate change to river impoundments. To address this 

limitation, future monitoring and research efforts should also 

include development and calibration of watershed models (for 

example, Precipitation-Runoff Modeling System) to estimate 

streamflow.

Personnel of NWRs throughout the northern Great Plains 

face management challenges associated with climate change, 

altered water supplies, and increasing salinity levels that have, 

or could potentially lead to, altered and diminished aquatic 

habitats that are critical to fulfilling a primary NWR System 

mission. To adequately address these challenges, wetland 

managers must be able to forecast the effects of various alterations to a system’s water balance in order to make informed 

decisions. The WSB model presented in this report can be 

used as a tool for evaluating alternative management goals 

and objectives by simulating important habitat characteristics 

of impoundments in light of changes to climate, management 

actions, and water availability.

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Appendixes 33

Appendixes
34 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Appendix 1. Description of model and input variables for the water and salt balance (WSB) model.

[The WSB model Excel workbook contains ten worksheets, four of which are the primary data input worksheets: model, climate, flows and 

management, and bathymetry. A description of all worksheets is provided in appendix 2. The ‘model’ sheet contains the water and salt balance 

(WSB) model. The ‘climate’ sheet includes climate data and evaporation model. The ‘flows and management’ sheet contains data relating to 

managed inflows, outflows, and water-control structure elevations. The ‘bathymetry’ sheet contains data relating depth, surface areas, volume, 

and pool elevation.NA, not applicable; NAVD 88, North American Vertical Datum of 1988; TDS, total dissolved solids; μS/cm, microsiemens 

per centimeter at 25 degrees Celsius; WCS, water-control structure]

Variable Units Variable definition/determination

Model worksheet

Date NA month/day/year

Pool elevation feet (NAVD 88) pool elevation of impoundment / initial value from field measurement or estimate; 

thereafter, value determined using lookup function (bathymetry worksheet) based 

on ‘final volume’ and ‘date’

Depth feet mean depth of impoundment / initial value determined using lookup function (bathymetry worksheet) based on ‘elevation’; thereafter, based on ‘final volume’ and 

‘date’

Surface area acres inundated surface area of impoundment / initial value determined using lookup 

function (bathymetry worksheet) based on ‘elevation’; thereafter, based on ‘final 

volume’ and ‘date’

Transition area acres noninundated surface area of impoundment (based on maximum area) / initial value 

determined using lookup function (bathymetry worksheet) based on ‘elevation’; 

thereafter, based on ‘final volume’ and ‘date’

Modeled volume acre-feet calculated volume of impoundment based on total water inputs and losses / initial 

value determined using lookup function (bathymetry worksheet) based on ‘elevation’; thereafter, calculated by adding ‘water input volume’ and subtracting ‘water 

losses’ from previous day’s ‘final volume’

Final volume acre-feet calculated volume of impoundment for daily time step; this variable “limits” the 

‘modeled volume’ based on ‘WCS volume’, if ‘modeled volume’ is greater than 

‘WCS volume’ the difference is considered outflow / value determine by subtracting ‘WCS volume’ from ‘modeled volume’

Specific conductance μS/cm specific conductance of impoundment water / initial value from field measurement or 

estimate; thereafter, calculated by converting ‘TDS’ using statistical relation (for 

example., fig. 2 [WSB model uses the following equation: 3.16TDS0.898])

TDS milligrams/

liter

total dissolved solids of impoundment water / initial value calculated by converting 

‘specific conductance’ using statistical relation (for example,, fig. 2 [WSB model 

uses the following equation: 0.319specific conductance1.1]); thereafter, calculated 

by dividing ‘salt mass’ by ‘final volume’

Salt mass milligrams total mass of salt dissolved in impoundment water / initial value calculated by multiplying ‘TDS’ by ‘modeled volume’; thereafter, mass is adjusted by adding ‘inflow 

salt mass’ and subtracting ‘outflow salt mass’

Precipitation inches measured precipitation / value determined using lookup function (climate worksheet) 

based on ‘date’

Inflow volume acre-feet managed (measured or estimated) inflow to impoundment / value determined using 

lookup function (flows and management worksheet) based on ‘date’

Inflow specific conductanceμS/cm specific conductance (measured or estimated) of ‘inflow volume’ / value determined 

using lookup function (flows and management worksheet) based on ‘date’

Water input volume acre-feet total daily water inputs to impoundment / calculated by adding ‘inflow volume’ and 

‘precipitation’ (‘precipitation’ is multiplied by ‘surface area’)

Evapotranspiration feet estimated evapotranspiration from impoundment / value determined using lookup 

function (climate worksheet) based on ‘date’; WSB model calculates evapotranspiration using the Jensen-Haise evaporation model, which requires air temperature 

and solar radiation

Outflow volume acre-feet managed (gaged or estimated) outflow from impoundment / value determined using 

lookup function (flows and management worksheet) based on ‘date’
Appendixes 35

Variable Units Variable definition/determination

Model worksheet—Continued

Water loss volume acre-feet total daily (gaged and estimated) water losses from impoundment / calculated by adding ‘outflow volume’ and ‘evapotranspiration’ (‘evapotranspiration’ is multiplied 

by ‘surface area’)

Inflow salt mass milligrams total mass of salt dissolved in ‘inflow volume’ / calculated by converting ‘specific 

conductance’ to ‘TDS’ using statistical relation (for example, fig. 2 [WSB model 

uses the following equation: 0.319specific conductance1.1]); ‘TDS’ is multiplied by 

‘inflow volume’

WCS outflow acre-feet volume of outflow based on water-control structure and pool elevations / calculated 

by subtracting ‘WCS volume’ from ‘modeled volume’; this variable is used only to 

calculate mass of salts lost to ‘uncontrolled’ outflow

Outflow salt mass milligrams total mass of salt in ‘outflow volume’ / calculated by converting ‘specific conductance’ to ‘TDS’ using statistical relation (for example, fig. 2 [WSB model uses the 

following equation: 0.319specific conductance1.1]); ‘TDS’ is multiplied by ‘outflow 

volume’ and ‘WCS outflow’

Bathymetry worksheet

Elevation feet (NAVD 88) surface (pool) elevation of impoundment

Volume acre-feet volume of impoundment

Surface area acres surface area of impoundment

Mean depth feet mean depth of impoundment

Exposed lakebed acres surface area of exposed lakebed (for example, mudflats)

Climate worksheet

Precipitation inches total daily precipitation

Air temperature degrees Fahrenheitmean daily air temperature

Solar radiation calories/square 

centimeter·day

mean daily solar radiation

Jensen-Haise inches estimated daily evaporation based on Jensen-Haise model

Evaporation inches estimated daily evaporation; if estimated value is less than zero evaporation is set as 

zero

Flows and Management worksheet

Inflow volume acre-feet surface inflow (gaged or estimated) to impoundment

Inflow specific conductanceμS/cm measured or estimated specific conductance of ‘inflow volume’; note: if there are 

inflows from more than one source with differing conductivities the model will 

have to be adjusted

Outflow volume acre-feet measured or estimated surface outflow from impoundment

WCS elevation feet (NAVD 88) water-control structure elevation

WCS volume acre-feet impoundment volume based on ‘WCS elevation’

Appendix 1. Description of model and input variables for the water and salt balance (WSB) model.—Continued

[The WSB model Excel workbook contains ten worksheets, four of which are the primary data input worksheets: model, climate, flows and 

management, and bathymetry. A description of all worksheets is provided in appendix 2. The ‘model’ sheet contains the water and salt balance 

(WSB) model. The ‘climate’ sheet includes climate data and evaporation model. The ‘flows and management’ sheet contains data relating to 

managed inflows, outflows, and water-control structure elevations. The ‘bathymetry’ sheet contains data relating depth, surface areas, volume, 

and pool elevation.NA, not applicable; NAVD 88, North American Vertical Datum of 1988; TDS, total dissolved solids; μS/cm, microsiemens 

per centimeter at 25 degrees Celsius; WCS, water-control structure]
36 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Appendix 2. Instructions for Using the Digital Water and Salt Balance Model 

for Managed Wetland Impoundments

(Jensen and Haise, 1963; McGuinness and Bordne, 1972; 

Rosenberry and others, 2004), but other equations or methods (for example, pan evaporation) can be easily substituted. 

Estimates of managed or natural inflows from canals and 

rivers are required, as are estimates of any managed outflows 

not accounted for by the primary water-control structure (for 

example, pumping). At a minimum, the WSB model requires 

elevation of the water-control structure to calculate surface 

outflows; however, when available, a stage-discharge curve 

will increase the accuracy of outflow rates. The model relies 

on a statistical relation (for example, fig. 2) to convert specific 

conductance to TDS, and vice-versa. Therefore, this relation 

must be specified by using site-specific data or selecting an 

appropriate model from existing literature. The WSB model 

incorporates the conversion model presented by Kendy (1999). 

Lastly, specific conductance and pool elevation are required to 

set initial model conditions.

Model Setup

To run the model a user must first adapt the WSB model 

to a specific site following five general steps: (1) Insert pool 

elevation, surface area, volume, and depth information into 

the ‘bathymetry’ sheet. Numerous model variables (depth, 

surface areas, pool elevation, volume) use a lookup function 

to obtain data from the ‘bathymetry’ sheet; thus, the cell range 

specified in the various lookup functions (‘model’ sheet) must 

be adjusted accordingly. (2) Insert daily data into the ‘climate’ 

sheet and insert any relevant information required to calculate 

evaporation (depends on method). Air temperature and solar 

radiation are required if using the Jensen-Haise equation associated with the WSB model. (3) Insert daily flow and watercontrol structure information into the ‘flows and management’ 

sheet. (4) Insert formula to convert specific conductance and 

TDS values into all appropriate cells (‘model’ and ‘starting 

values’ sheets). (5) Insert specific conductance and pool elevation into the ‘starting values’ sheet.

Once the bathymetric, daily input, conversion model, 

and starting values data are inserted, adjust the date range in 

the ‘model’ sheet so that it matches the input data sheets. The 

first row in the ‘model’ sheet is unique because it reads-in data 

from the starting values sheet. All subsequent rows are similar 

and the second row can be “filled down” for all remaining 

rows (based on the date range). Similarly, adjust the axes (data 

and date) in the ‘graph’ sheets to match the data range in the 

‘model’ sheet.

Overview

A digital water and salt balance (WSB) model was developed to simulate various habitat metrics for managed wetland 

impoundments. The WSB model was developed in Microsoft 

Excel 2010; thus, a basic proficiency with the program is 

beneficial. The WSB model is available at http://pubs.usgs.

gov/sir/2013/5114/. The Excel workbook contains ten worksheets: (1) model variables, (2) input variables, (3) bathymetry, (4) climate, (5) flows and management, (6) starting 

values, (7) model, (8) graph 1, (9) graph 2, and (10) graph 3. 

Each worksheet variable is described in detail in appendix 1. 

The following paragraph provides a brief overview of each 

worksheet.

The ‘model variables’ sheet describes each model variable, specifies the unit of measure, and describes how the 

value is determined. The ‘input variables’ sheet lists and 

defines the variables for each input worksheet (bathymetry, 

climate, flows and management). The ‘bathymetry’ sheet 

contains the depth, surface area, and volume data; each variable is presented twice in this worksheet to facilitate various 

lookup functions from the model. The ‘climate’ sheet includes 

daily precipitation and any additional data or models required 

to calculate evaporation (for example, temperature, solar 

radiation). The ‘flows and management’ sheet includes daily 

water inflow (if managed), specific conductance of the inflow 

water, daily outflow (if managed), water-control structure 

elevation, and a maximum water volume based on the watercontrol structure elevation and bathymetric data. The ‘starting 

values’ sheet specifies specific conductance, total dissolved 

solids (TDS), and pool elevation for initial model conditions. 

The ‘model’ sheet contains the WSB model; all calculations 

and lookup functions are embedded in the cell formulas and 

described in appendix 1. The three ‘graph’ sheets depict (1) 

daily specific conductance and pool elevation, (2) daily depth 

and surface areas (inundated, dry), and (3) daily mass of dissolved salts.

Input Data

Prior to running the model the following data must be 

incorporated. At a minimum, the model requires a rough 

surface area-capacity-depth curve, measured or modeled 

precipitation, and other data to support estimates of evaporation (for example, temperature, solar radiation). The WSB 

model calculates evaporation using the Jensen-Haise equation 
Appendixes 37

Adapting the Water and Salt Balance 

Model

The model is formatted and structured to facilitate 

adaptation to specific impoundments that vary according to 

available data. If additional information is available, a vari-

able column can simply be added and incorporated into the 

existing model structure. For example, if a stage-discharge 

curve is available to calculate surface outflows (for example, 

Sand Lake National Wildlife Refuge and Long Lake National 

Wildlife Refuge model validations), a column (and formula) 

can be added, and the resulting estimate can be added to the 

“outflow” variable. Similarly, if daily data are not available, 

the model can easily be adjusted to provide monthly output. 

With this simple and transparent structure, nearly any variable 

associated with the water and salt balance of an impound-

ment can be added (or subtracted) with minimal technical 

programming.
38 Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments

Publishing support provided by: 

Rolla and Lafayette Publishing Service Centers 

For more information concerning this publication, contact:

Director, USGS Northern Prairie Wildlife Research Center

8711 37th Street Southeast

Jamestown, North Dakota 58401

(701) 253–5553

Or visit the Northern Prairie Wildlife Research Center Web site at:

http://www.npwrc.usgs.gov/

Tangen and others— Model for Evaluating Climate, Water Availability, and Water Management on Wetland Impoundments—SIR 2013–5114